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top</button><!----></div></div><aside class="VPSidebar" data-v-83f63849 data-v-0e47c5d5><div class="curtain" data-v-0e47c5d5></div><nav class="nav" id="VPSidebarNav" aria-labelledby="sidebar-aria-label" tabindex="-1" data-v-0e47c5d5><span class="visually-hidden" id="sidebar-aria-label" data-v-0e47c5d5> Sidebar Navigation </span><!--[--><!--]--><!--[--><div class="group" data-v-0e47c5d5><section class="VPSidebarItem level-0 collapsible has-active" data-v-0e47c5d5 data-v-0cc45b6b><div class="item" role="button" tabindex="0" data-v-0cc45b6b><div class="indicator" data-v-0cc45b6b></div><h2 class="text" data-v-0cc45b6b>IPhO Formulas: JP Ver.</h2><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-0cc45b6b><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="caret-icon" data-v-0cc45b6b><path 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data-v-0cc45b6b><div class="item" data-v-0cc45b6b><div class="indicator" data-v-0cc45b6b></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/3" data-v-0cc45b6b data-v-075865b7><!--[--><p class="text" data-v-0cc45b6b>3: 運動学</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-0cc45b6b data-v-0cc45b6b><div class="item" data-v-0cc45b6b><div class="indicator" data-v-0cc45b6b></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/4" data-v-0cc45b6b data-v-075865b7><!--[--><p class="text" data-v-0cc45b6b>4: 力学</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-0cc45b6b data-v-0cc45b6b><div class="item" data-v-0cc45b6b><div class="indicator" data-v-0cc45b6b></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/5" data-v-0cc45b6b data-v-075865b7><!--[--><p class="text" data-v-0cc45b6b>5: 振動と波</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-0cc45b6b data-v-0cc45b6b><div class="item" data-v-0cc45b6b><div class="indicator" data-v-0cc45b6b></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/6" data-v-0cc45b6b data-v-075865b7><!--[--><p class="text" data-v-0cc45b6b>6: 幾何光学，測光</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-0cc45b6b data-v-0cc45b6b><div class="item" data-v-0cc45b6b><div class="indicator" data-v-0cc45b6b></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/7" data-v-0cc45b6b data-v-075865b7><!--[--><p class="text" data-v-0cc45b6b>7: 波動光学</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link is-active has-active" data-v-0cc45b6b data-v-0cc45b6b><div class="item" data-v-0cc45b6b><div class="indicator" data-v-0cc45b6b></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/8" data-v-0cc45b6b data-v-075865b7><!--[--><p class="text" data-v-0cc45b6b>8: 電気回路</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-0cc45b6b data-v-0cc45b6b><div class="item" data-v-0cc45b6b><div class="indicator" data-v-0cc45b6b></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/9" data-v-0cc45b6b data-v-075865b7><!--[--><p class="text" data-v-0cc45b6b>9: 電磁気学</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-0cc45b6b data-v-0cc45b6b><div class="item" data-v-0cc45b6b><div class="indicator" data-v-0cc45b6b></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/10" data-v-0cc45b6b data-v-075865b7><!--[--><p class="text" data-v-0cc45b6b>10: 熱力</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-0cc45b6b data-v-0cc45b6b><div class="item" data-v-0cc45b6b><div 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相対性理論</p><!--]--><!----></a><!----></div><!----></div><!--]--></div></section></div><!--]--><!--[--><!--]--></nav></aside><div class="VPContent has-sidebar" id="VPContent" data-v-83f63849 data-v-bb292142><div class="VPDoc has-sidebar has-aside" data-v-bb292142 data-v-6c4a7022><!--[--><!--]--><div class="container" data-v-6c4a7022><div class="aside" data-v-6c4a7022><div class="aside-curtain" data-v-6c4a7022></div><div class="aside-container" data-v-6c4a7022><div class="aside-content" data-v-6c4a7022><div class="VPDocAside" data-v-6c4a7022 data-v-f77a9b1a><!--[--><!--]--><!--[--><!--]--><div class="VPDocAsideOutline" data-v-f77a9b1a data-v-ea95c6a2><div class="content" data-v-ea95c6a2><div class="outline-marker" data-v-ea95c6a2></div><div class="outline-title" data-v-ea95c6a2>TOC</div><nav aria-labelledby="doc-outline-aria-label" data-v-ea95c6a2><span class="visually-hidden" id="doc-outline-aria-label" data-v-ea95c6a2> Table of Contents for current page </span><ul class="root" 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class="vp-doc _academic_physics_ipho-formulas-jpn_8" data-v-6c4a7022><div><h1 id="formulas-for-ipho-日本語版-section-8" tabindex="-1">Formulas for IPhO 日本語版: Section 8 <a class="header-anchor" href="#formulas-for-ipho-日本語版-section-8" aria-label="Permalink to "Formulas for IPhO 日本語版: Section 8""></a></h1><h2 id="_8-電気回路" tabindex="-1">8: 電気回路 <a class="header-anchor" href="#_8-電気回路" aria-label="Permalink to "8: 電気回路""></a></h2><h3 id="_8-1-v-i-r-p-v-i" tabindex="-1">8.1: V=I R, P=V I <a class="header-anchor" href="#_8-1-v-i-r-p-v-i" aria-label="Permalink to "8.1: V=I R, P=V I""></a></h3><ol><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mi>I</mi><mi>R</mi><mo separator="true">,</mo><mi>P</mi><mo>=</mo><mi>V</mi><mi>I</mi></mrow><annotation encoding="application/x-tex">V=I R, P=V I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span></span></span></span><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>R</mi><mtext>直列 </mtext></msub><mo>=</mo><mo>∑</mo><msub><mi>R</mi><mi>i</mi></msub><mo separator="true">,</mo><msubsup><mi>R</mi><mtext>並列 </mtext><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mo>=</mo><mo>∑</mo><msubsup><mi>R</mi><mi>i</mi><mrow><mo>−</mo><mn>1</mn></mrow></msubsup></mrow><annotation encoding="application/x-tex">R_{\text {直列 }}=\sum R_i, R_{\text {並列 }}^{-1}=\sum R_i^{-1} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord cjk_fallback mtight">直列</span><span class="mord mtight"> </span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.6em;vertical-align:-0.55em;"></span><span class="mop op-symbol large-op" style="position:relative;top:0em;">∑</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-2.4163em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord cjk_fallback mtight">並列</span><span class="mord mtight"> </span></span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2837em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.6em;vertical-align:-0.55em;"></span><span class="mop op-symbol large-op" style="position:relative;top:0em;">∑</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-2.433em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.267em;"><span></span></span></span></span></span></span></span></span></span></span></p></li></ol><h3 id="_8-2-kirchhoff-の法則" tabindex="-1">8.2: Kirchhoff の法則 <a class="header-anchor" href="#_8-2-kirchhoff-の法則" aria-label="Permalink to "8.2: Kirchhoff の法則""></a></h3><ol start="2"><li>Kirchhoff の法則 :<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><munder><mo>∑</mo><mstyle scriptlevel="1"><mtable rowspacing="0.1em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="1" displaystyle="false"><mtext> 節点 </mtext></mstyle></mtd></mtr></mtable></mstyle></munder><mi>I</mi><mo>=</mo><mn>0</mn><mo separator="true">,</mo><munder><mo>∑</mo><mtext>閉路 </mtext></munder><mi>V</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\sum_{\substack{\text { 節点 }}} I=0, \sum_{\text {閉路 }} V=0 </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4703em;vertical-align:-1.4203em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.05em;"><span style="top:-1.8568em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6817em;"><span style="top:-2.6983em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight"> </span><span class="mord cjk_fallback mtight">節点</span><span class="mord mtight"> </span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1817em;"><span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.4203em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.3443em;vertical-align:-1.2943em;"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.05em;"><span style="top:-1.8557em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord cjk_fallback mtight">閉路</span><span class="mord mtight"> </span></span></span></span></span><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.2943em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></li></ol><h3 id="_8-3-ポイント-2-の方程式を減らすために" tabindex="-1">8.3: ポイント 2 の方程式を減らすために <a class="header-anchor" href="#_8-3-ポイント-2-の方程式を減らすために" aria-label="Permalink to "8.3: ポイント 2 の方程式を減らすために""></a></h3><ol start="3"><li>ポイント 2 の方程式を減らすために: 節点電位法. ルー プ電流法. 等価回路 (3 端子の場合 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo><mi mathvariant="normal">△</mi><mtext>又</mtext></mrow><annotation encoding="application/x-tex">\Rightarrow \triangle 又</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">⇒</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">△</span><span class="mord cjk_fallback">又</span></span></span></span> 又 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">Y</span></span></span></span> の形, 起電力のある 2 端子の場合 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> 抵抗と電池の直列)</li></ol><h3 id="_8-4-無限につながる抵抗" tabindex="-1">8.4: 無限につながる抵抗 <a class="header-anchor" href="#_8-4-無限につながる抵抗" aria-label="Permalink to "8.4: 無限につながる抵抗""></a></h3><ol start="4"><li>無限につながる抵抗 : 無限に続く格子の隣り合う節点 間で，自己相似性を使う。鏡像法の一般化された方法.</li></ol><h3 id="_8-5-交流回路" tabindex="-1">8.5: 交流回路 <a class="header-anchor" href="#_8-5-交流回路" aria-label="Permalink to "8.5: 交流回路""></a></h3><ol start="5"><li>交流回路: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi></mrow><annotation encoding="application/x-tex">R</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span></span></span></span> を <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Z</mi></mrow><annotation encoding="application/x-tex">Z</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">Z</span></span></span></span> に置き換えてポイント <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo>∼</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">1 \sim 4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">4</span></span></span></span> を用 いる.<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="center" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><msub><mi>Z</mi><mi>R</mi></msub><mo>=</mo><mi>R</mi><mo separator="true">,</mo><msub><mi>Z</mi><mi>C</mi></msub><mo>=</mo><mn>1</mn><mi mathvariant="normal">/</mi><mi>i</mi><mi>ω</mi><mi>C</mi><mo separator="true">,</mo><msub><mi>Z</mi><mi>L</mi></msub><mo>=</mo><mi>i</mi><mi>ω</mi><mi>L</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>φ</mi><mo>=</mo><mi>arg</mi><mo></mo><mi>Z</mi><mo separator="true">,</mo><msub><mi>V</mi><mtext>eff </mtext></msub><mo>=</mo><mi mathvariant="normal">∣</mi><mi>Z</mi><mi mathvariant="normal">∣</mi><msub><mi>I</mi><mtext>eff </mtext></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>P</mi><mo>=</mo><mi mathvariant="normal">∣</mi><mi>V</mi><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><mi>I</mi><mi mathvariant="normal">∣</mi><mi>cos</mi><mo></mo><mo stretchy="false">(</mo><mi>arg</mi><mo></mo><mi>Z</mi><mo stretchy="false">)</mo><mo>=</mo><mo>∑</mo><msubsup><mi>I</mi><mi>i</mi><mn>2</mn></msubsup><msub><mi>R</mi><mi>i</mi></msub></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{gathered} Z_R=R, Z_C=1 / i \omega C, Z_L=i \omega L \\ \varphi=\arg Z, V_{\text {eff }}=|Z| I_{\text {eff }} \\ P=|V||I| \cos (\arg Z)=\sum I_i^2 R_i \end{gathered} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.9em;vertical-align:-2.2em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.7em;"><span style="top:-4.91em;"><span class="pstrut" style="height:3.05em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">Z</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.00773em;">R</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">Z</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07153em;">C</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">1/</span><span class="mord mathnormal" style="margin-right:0.03588em;">iω</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">Z</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">L</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">iω</span><span class="mord mathnormal">L</span></span></span><span style="top:-3.41em;"><span class="pstrut" style="height:3.05em;"></span><span class="mord"><span class="mord mathnormal">φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop">ar<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">Z</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">eff </span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.07153em;">Z</span><span class="mord">∣</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">eff </span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-1.7em;"><span class="pstrut" style="height:3.05em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mord">∣∣</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord">∣</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">cos</span><span class="mopen">(</span><span class="mop">ar<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">Z</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop op-symbol large-op" style="position:relative;top:0em;">∑</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-2.453em;margin-left:-0.0785em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.2em;"><span></span></span></span></span></span></span></span></span></span></span></span></p></li></ol><h3 id="_8-6-特性時間" tabindex="-1">8.6: 特性時間 <a class="header-anchor" href="#_8-6-特性時間" aria-label="Permalink to "8.6: 特性時間""></a></h3><ol start="6"><li>特性時間: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>τ</mi><mrow><mi>R</mi><mi>C</mi></mrow></msub><mo>=</mo><mi>R</mi><mi>C</mi><mo separator="true">,</mo><msub><mi>τ</mi><mrow><mi>L</mi><mi>R</mi></mrow></msub><mo>=</mo><mi>L</mi><mi mathvariant="normal">/</mi><mi>R</mi><mi mathvariant="normal">.</mi><msub><mi>ω</mi><mrow><mi>L</mi><mi>C</mi></mrow></msub><mo>=</mo></mrow><annotation encoding="application/x-tex">\tau_{R C}=R C, \tau_{L R}=L / R . \omega_{L C}=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1132em;">τ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1132em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.07153em;">RC</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">RC</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1132em;">τ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1132em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span><span class="mord mathnormal mtight" style="margin-right:0.00773em;">R</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mord">/</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mord">.</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span><span class="mord mathnormal mtight" style="margin-right:0.07153em;">C</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mi mathvariant="normal">/</mi><msqrt><mrow><mi>L</mi><mi>C</mi></mrow></msqrt></mrow><annotation encoding="application/x-tex">1 / \sqrt{L C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1767em;vertical-align:-0.25em;"></span><span class="mord">1/</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9267em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span></span></span><span style="top:-2.8867em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
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M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1133em;"><span></span></span></span></span></span></span></span></span>. 定常的な電流分布への緩和は指数関数的で <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∝</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>t</mi><mi mathvariant="normal">/</mi><mi>τ</mi></mrow></msup></mrow><annotation encoding="application/x-tex">\propto e^{-t / \tau}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.888em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">t</span><span class="mord mtight">/</span><span class="mord mathnormal mtight" style="margin-right:0.1132em;">τ</span></span></span></span></span></span></span></span></span></span></span></span></li></ol><h3 id="_8-7-電気回路のエネルギー保存則" tabindex="-1">8.7: 電気回路のエネルギー保存則 <a class="header-anchor" href="#_8-7-電気回路のエネルギー保存則" aria-label="Permalink to "8.7: 電気回路のエネルギー保存則""></a></h3><ol start="8"><li>電気回路のエネルギー保存則 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>W</mi><mo>+</mo><mi>Q</mi><mo>=</mo><mi>q</mi><mi>V</mi></mrow><annotation encoding="application/x-tex">\Delta W+Q=q V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord">Δ</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">Q</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span></span></span></span>. ここ で <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span></span> は電圧降下 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow><annotation encoding="application/x-tex">V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span></span></span></span> を通った電気量で, 電源のする仕事 は <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>=</mo><mi>q</mi><msub><mi>V</mi><mrow><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">f</mi></mrow></msub></mrow><annotation encoding="application/x-tex">A=q V_{\mathrm{emf}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathrm mtight" style="margin-right:0.07778em;">emf</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li></ol><h3 id="_8-8-コンデンサーの位置エネルギー式" tabindex="-1">8.8: コンデンサーの位置エネルギー式 <a class="header-anchor" href="#_8-8-コンデンサーの位置エネルギー式" aria-label="Permalink to "8.8: コンデンサーの位置エネルギー式""></a></h3><ol start="8"><li>コンデンサーの位置エネルギー式: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>W</mi><mi>C</mi></msub><mo>=</mo><mi>C</mi><msup><mi>V</mi><mn>2</mn></msup><mi mathvariant="normal">/</mi><mn>2</mn><mo separator="true">,</mo><msub><mi>W</mi><mi>L</mi></msub><mo>=</mo><mi>L</mi><msup><mi>I</mi><mn>2</mn></msup><mi mathvariant="normal">/</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">W_C=C V^2 / 2, W_L=L I^2 / 2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07153em;">C</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord">/2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">L</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord">/2</span></span></span></span>.</li></ol><h3 id="_8-9-磁束密度" tabindex="-1">8.9: 磁束密度 <a class="header-anchor" href="#_8-9-磁束密度" aria-label="Permalink to "8.9: 磁束密度""></a></h3><ol start="9"><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">f</mi></mrow></msub><mo>=</mo><mo>−</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">Φ</mi><mi mathvariant="normal">/</mi><mi mathvariant="normal">d</mi><mi>t</mi><mo>=</mo><mi mathvariant="normal">d</mi><mo stretchy="false">(</mo><mi>L</mi><mi>I</mi><mo stretchy="false">)</mo><mi mathvariant="normal">/</mi><mi mathvariant="normal">d</mi><mi>t</mi><mo separator="true">,</mo><mi mathvariant="normal">Φ</mi><mo>=</mo><mi>B</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">V_{\mathrm{emf}}=-\mathrm{d} \Phi / \mathrm{d} t=\mathrm{d}(L I) / \mathrm{d} t, \Phi=B S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathrm mtight" style="margin-right:0.07778em;">emf</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">−</span><span class="mord mathrm">d</span><span class="mord">Φ/</span><span class="mord mathrm">d</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathrm">d</span><span class="mopen">(</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mclose">)</span><span class="mord">/</span><span class="mord mathrm">d</span><span class="mord mathnormal">t</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">Φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">BS</span></span></span></span>.</li></ol><h3 id="_8-10-非線形素子" tabindex="-1">8.10: 非線形素子 <a class="header-anchor" href="#_8-10-非線形素子" aria-label="Permalink to "8.10: 非線形素子""></a></h3><ol start="10"><li>非 線形素子: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>−</mo><mi>I</mi></mrow><annotation encoding="application/x-tex">V-I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span></span></span></span> グラフでの非線形曲線と Ohm/Kirchhoff の法則を表す直線との交点として 为形的に解を求める. 複数の交点があれば安定性を調 ベる. いくつかの解は普通安定でない.</li></ol><h3 id="_8-11-短時間と長時間の極限を利用" tabindex="-1">8.11: 短時間と長時間の極限を利用 <a class="header-anchor" href="#_8-11-短時間と長時間の極限を利用" aria-label="Permalink to "8.11: 短時間と長時間の極限を利用""></a></h3><ol start="11"><li>短時間と長時間の極限を利用する: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mtext>observation </mtext></msub><mo>≫</mo></mrow><annotation encoding="application/x-tex">t_{\text {observation }} \gg</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7651em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">observation </span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≫</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>τ</mi><mrow><mi>R</mi><mi>C</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\tau_{R C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1132em;">τ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1132em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.07153em;">RC</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> or <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>τ</mi><mrow><mi>L</mi><mi>R</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\tau_{L R}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1132em;">τ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1132em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span><span class="mord mathnormal mtight" style="margin-right:0.00773em;">R</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> ならば, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>I</mi><mi>C</mi></msub><mo>≈</mo><mn>0</mn><mo stretchy="false">(</mo><mi>C</mi></mrow><annotation encoding="application/x-tex">I_C \approx 0(C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07153em;">C</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span></span></span></span> は断線している）又 は <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>L</mi></msub><mo>≈</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">V_L \approx 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">L</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span> ( <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi></mrow><annotation encoding="application/x-tex">L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">L</span></span></span></span> は短絡している）のような準平衡状態に 達する. <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mtext>observation </mtext></msub><mo>≪</mo><msub><mi>τ</mi><mrow><mi>R</mi><mi>C</mi></mrow></msub></mrow><annotation encoding="application/x-tex">t_{\text {observation }} \ll \tau_{R C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7651em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">observation </span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≪</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1132em;">τ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1132em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.07153em;">RC</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> or <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>τ</mi><mrow><mi>L</mi><mi>R</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\tau_{L R}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1132em;">τ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1132em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span><span class="mord mathnormal mtight" style="margin-right:0.00773em;">R</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> ならば, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span></span></span></span> の電 気量の変化や <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi></mrow><annotation encoding="application/x-tex">L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">L</span></span></span></span> での電流の変化は小さく, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>Q</mi><mo>≪</mo><mi>Q</mi></mrow><annotation encoding="application/x-tex">\Delta Q \ll Q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord">Δ</span><span class="mord mathnormal">Q</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≪</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">Q</span></span></span></span> や <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>I</mi><mo>≪</mo><mi>I</mi></mrow><annotation encoding="application/x-tex">\Delta I \ll I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em;"></span><span class="mord">Δ</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≪</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span></span></span></span>. 即ち <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span></span></span></span> は短絡していて <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi></mrow><annotation encoding="application/x-tex">L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">L</span></span></span></span> は断線して いる.</li></ol><h3 id="_8-12-推論" tabindex="-1">8.12: 推論 <a class="header-anchor" href="#_8-12-推論" aria-label="Permalink to "8.12: 推論""></a></h3><ol start="12"><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mo mathvariant="normal">≠</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">L \neq 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">L</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mrel"><span class="mord vbox"><span class="thinbox"><span class="rlap"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="inner"><span class="mord"><span class="mrel"></span></span></span><span class="fix"></span></span></span></span></span><span class="mrel">=</span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span> ならば, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">I(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span> は連続.</li></ol><h3 id="_8-13-超電導の回路" tabindex="-1">8.13: 超電導の回路 <a class="header-anchor" href="#_8-13-超電導の回路" aria-label="Permalink to "8.13: 超電導の回路""></a></h3><ol start="13"><li>超電導の回路について, 磁束 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Φ</mi><mo>=</mo></mrow><annotation encoding="application/x-tex">\Phi=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span></span></span></span> const.. 特に, 外部 磁場が無ければ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>I</mi><mo>=</mo></mrow><annotation encoding="application/x-tex">L I=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span></span></span></span> const.</li></ol><h3 id="_8-14-相互誘導" tabindex="-1">8.14: 相互誘導 <a class="header-anchor" href="#_8-14-相互誘導" aria-label="Permalink to "8.14: 相互誘導""></a></h3><ol start="14"><li>相互誘導 : 回路 1 を通る磁束は <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="normal">Φ</mi><mn>1</mn></msub><mo>=</mo><msub><mi>L</mi><mn>1</mn></msub><msub><mi>I</mi><mn>1</mn></msub><mo>+</mo><msub><mi>L</mi><mn>12</mn></msub><msub><mi>I</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\Phi_1=L_1 I_1+L_{12} I_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord">Φ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">12</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> ( <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>I</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">I_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> は回路 2 を流れる電流) で, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mn>12</mn></msub><mo>=</mo><msub><mi>L</mi><mn>21</mn></msub><mo>≡</mo><mi>M</mi></mrow><annotation encoding="application/x-tex">L_{12}=L_{21} \equiv M</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">12</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">21</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≡</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span></span></span></span> と <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mo>≤</mo><msqrt><mrow><msub><mi>L</mi><mn>1</mn></msub><msub><mi>L</mi><mn>2</mn></msub></mrow></msqrt></mrow><annotation encoding="application/x-tex">M \leq \sqrt{L_1 L_2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8193em;vertical-align:-0.136em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.04em;vertical-align:-0.1883em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8517em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" 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