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<blockquote data-quote="AnuradhaRa" data-source="post: 31120930" data-attributes="member: 325076"><p>Ah! Now I understand exactly what you’re asking — you are focusing on the <strong>cause-and-effect loop between current change and back EMF</strong>, independent of the applied voltage. Let’s clarify carefully.</p><hr /><h3><img class="smilie smilie--emoji" loading="lazy" alt="🔑" title="Key :key:" src="https://cdn.jsdelivr.net/joypixels/assets/6.6/png/unicode/64/1f511.png" data-shortname=":key:" /> Key principle</h3><p><strong>Back EMF (V_back) is caused by the rate of change of current:</strong></p><p>Vback=−LdIdtV_\text{back} = -L \frac{dI}{dt}Vback=−LdtdI</p><ul> <li data-xf-list-type="ul">If current is constant → no back EMF</li> <li data-xf-list-type="ul">If current changes → back EMF appears</li> <li data-xf-list-type="ul">Faster change → stronger back EMF</li> </ul><p>So you are right: <strong>the back EMF depends on dI/dt, not directly on voltage.</strong></p><hr /><h3><img class="smilie smilie--emoji" loading="lazy" alt="🧩" title="Puzzle piece :jigsaw:" src="https://cdn.jsdelivr.net/joypixels/assets/6.6/png/unicode/64/1f9e9.png" data-shortname=":jigsaw:" /> The “chicken-and-egg” question</h3><p>You’re asking:</p><p></p><p>This is subtle but important.</p><hr /><h3><span style="font-size: 18px"><span style="color: rgb(247, 218, 100)"><img class="smilie smilie--emoji" loading="lazy" alt="1️⃣" title="Keycap: 1 :one:" src="https://cdn.jsdelivr.net/joypixels/assets/6.6/png/unicode/64/0031-20e3.png" data-shortname=":one:" /> The initiating factor is <strong>applied voltage</strong></span></span></h3><p><span style="font-size: 18px"><span style="color: rgb(251, 160, 38)">Even though back EMF depends on dI/dt, the <strong>rate of current change itself is forced by the applied voltage</strong>.</span></span></p><p><span style="font-size: 18px"><span style="color: rgb(247, 218, 100)">From Kirchhoff’s law for an RL series circuit:</span></span></p><p><span style="font-size: 18px"><span style="color: rgb(247, 218, 100)">Vapplied=IR+LdIdtV_\text{applied} = I R + L \frac{dI}{dt}Vapplied=IR+LdtdI</span></span></p><p><span style="font-size: 18px"><span style="color: rgb(247, 218, 100)">Rewriting:</span></span></p><p><span style="font-size: 18px"><span style="color: rgb(247, 218, 100)">dIdt=Vapplied−IRL\frac{dI}{dt} = \frac{V_\text{applied} - I R}{L}dtdI=LVapplied−IR</span></span></p><ul> <li data-xf-list-type="ul"><span style="font-size: 18px"><span style="color: rgb(247, 218, 100)">At t = 0, I = 0 → dIdt=VappliedL\frac{dI}{dt} = \frac{V_\text{applied}}{L}dtdI=LVapplied</span></span></li> <li data-xf-list-type="ul"><span style="font-size: 18px"><span style="color: rgb(247, 218, 100)">So the applied voltage <strong>starts the current changing</strong>, and <strong>that change produces back EMF</strong>.</span></span></li> </ul><p><span style="font-size: 18px"><span style="color: rgb(247, 218, 100)">So:</span></span></p><p><span style="font-size: 18px"><span style="color: rgb(247, 218, 100)"><strong>Applied voltage → causes initial dI/dt → produces back EMF → slows dI/dt</strong></span></span></p><hr /><h3><img class="smilie smilie--emoji" loading="lazy" alt="2️⃣" title="Keycap: 2 :two:" src="https://cdn.jsdelivr.net/joypixels/assets/6.6/png/unicode/64/0032-20e3.png" data-shortname=":two:" /> The inductor resists change</h3> <ul> <li data-xf-list-type="ul">Once current starts rising, the inductor generates back EMF</li> <li data-xf-list-type="ul">This reduces the effective voltage pushing current: Veffective=Vapplied−VbackV_\text{effective} = V_\text{applied} - V_\text{back}Veffective=Vapplied−Vback</li> <li data-xf-list-type="ul">Therefore, dI/dt decreases over time</li> </ul><p>This is why the current rises gradually.</p><hr /><h3><img class="smilie smilie--emoji" loading="lazy" alt="⚡" title="High voltage :zap:" src="https://cdn.jsdelivr.net/joypixels/assets/6.6/png/unicode/64/26a1.png" data-shortname=":zap:" /> Analogy</h3><p>Think of water in a tank:</p><ul> <li data-xf-list-type="ul">You open a faucet (applied voltage) → water starts flowing (current starts changing)</li> <li data-xf-list-type="ul">A valve resists flow proportionally to the flow rate (back EMF resists dI/dt)</li> <li data-xf-list-type="ul">Flow rises slowly until steady state</li> </ul><hr /><h3><img class="smilie smilie--emoji" loading="lazy" alt="✅" title="Check mark button :white_check_mark:" src="https://cdn.jsdelivr.net/joypixels/assets/6.6/png/unicode/64/2705.png" data-shortname=":white_check_mark:" /> <strong>The subtle point</strong></h3> <ul> <li data-xf-list-type="ul"><strong>Cause of back EMF:</strong> rate of current change (dI/dtdI/dtdI/dt)</li> <li data-xf-list-type="ul"><strong>Cause of current change in the first place:</strong> applied voltage</li> <li data-xf-list-type="ul"><strong>Effect:</strong> back EMF reduces rate of change</li> </ul><p>So yes, back EMF <strong>does not itself create current change</strong>; it <strong>resists it</strong>. The voltage source is what “forces” the initial change.</p><hr /><p>If you want, I can draw a <strong>timeline diagram showing voltage, dI/dt, and back EMF together</strong>, which usually clears this confusion instantly.</p><p>Do you want me to do that?</p></blockquote><p></p>
[QUOTE="AnuradhaRa, post: 31120930, member: 325076"] Ah! Now I understand exactly what you’re asking — you are focusing on the [B]cause-and-effect loop between current change and back EMF[/B], independent of the applied voltage. Let’s clarify carefully. [HR][/HR] [HEADING=2]🔑 Key principle[/HEADING] [B]Back EMF (V_back) is caused by the rate of change of current:[/B] Vback=−LdIdtV_\text{back} = -L \frac{dI}{dt}Vback=−LdtdI [LIST] [*]If current is constant → no back EMF [*]If current changes → back EMF appears [*]Faster change → stronger back EMF [/LIST] So you are right: [B]the back EMF depends on dI/dt, not directly on voltage.[/B] [HR][/HR] [HEADING=2]🧩 The “chicken-and-egg” question[/HEADING] You’re asking: This is subtle but important. [HR][/HR] [HEADING=2][SIZE=5][COLOR=rgb(247, 218, 100)]1️⃣ The initiating factor is [B]applied voltage[/B][/COLOR][/SIZE][/HEADING] [SIZE=5][COLOR=rgb(251, 160, 38)]Even though back EMF depends on dI/dt, the [B]rate of current change itself is forced by the applied voltage[/B].[/COLOR] [COLOR=rgb(247, 218, 100)]From Kirchhoff’s law for an RL series circuit: Vapplied=IR+LdIdtV_\text{applied} = I R + L \frac{dI}{dt}Vapplied=IR+LdtdI Rewriting: dIdt=Vapplied−IRL\frac{dI}{dt} = \frac{V_\text{applied} - I R}{L}dtdI=LVapplied−IR[/COLOR][/SIZE] [LIST] [*][SIZE=5][COLOR=rgb(247, 218, 100)]At t = 0, I = 0 → dIdt=VappliedL\frac{dI}{dt} = \frac{V_\text{applied}}{L}dtdI=LVapplied[/COLOR][/SIZE] [*][SIZE=5][COLOR=rgb(247, 218, 100)]So the applied voltage [B]starts the current changing[/B], and [B]that change produces back EMF[/B].[/COLOR][/SIZE] [/LIST] [SIZE=5][COLOR=rgb(247, 218, 100)]So: [B]Applied voltage → causes initial dI/dt → produces back EMF → slows dI/dt[/B][/COLOR][/SIZE] [HR][/HR] [HEADING=2]2️⃣ The inductor resists change[/HEADING] [LIST] [*]Once current starts rising, the inductor generates back EMF [*]This reduces the effective voltage pushing current: Veffective=Vapplied−VbackV_\text{effective} = V_\text{applied} - V_\text{back}Veffective=Vapplied−Vback [*]Therefore, dI/dt decreases over time [/LIST] This is why the current rises gradually. [HR][/HR] [HEADING=2]⚡ Analogy[/HEADING] Think of water in a tank: [LIST] [*]You open a faucet (applied voltage) → water starts flowing (current starts changing) [*]A valve resists flow proportionally to the flow rate (back EMF resists dI/dt) [*]Flow rises slowly until steady state [/LIST] [HR][/HR] [HEADING=2]✅ [B]The subtle point[/B][/HEADING] [LIST] [*][B]Cause of back EMF:[/B] rate of current change (dI/dtdI/dtdI/dt) [*][B]Cause of current change in the first place:[/B] applied voltage [*][B]Effect:[/B] back EMF reduces rate of change [/LIST] So yes, back EMF [B]does not itself create current change[/B]; it [B]resists it[/B]. The voltage source is what “forces” the initial change. [HR][/HR] If you want, I can draw a [B]timeline diagram showing voltage, dI/dt, and back EMF together[/B], which usually clears this confusion instantly. Do you want me to do that? [/QUOTE]
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