Derive the formula for equivalent capacitance in series combination.

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Accepted Answer

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> [!TLDR]
> In a series combination each capacitor carries the same charge but a different voltage; summing the voltages and using $V=Q/C$ gives the series formula for equivalent capacitance.
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> **Equivalent capacitance for capacitors in series**
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> Consider three capacitors of capacitances $C_1$, $C_2$, $C_3$ connected in series across a battery of EMF $V$.
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> **Key property of series connection:** the same charge $Q$ flows through and gets stored on each capacitor (since they are connected end-to-end and the same current flows through the single series path while charging).
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> The potential difference across each capacitor is then:
> $$V_1 = \dfrac{Q}{C_1}, \quad V_2 = \dfrac{Q}{C_2}, \quad V_3 = \dfrac{Q}{C_3}$$
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> The total potential difference (applied EMF) equals the sum of the individual potential drops:
> $$V = V_1 + V_2 + V_3 = Q\left(\dfrac{1}{C_1} + \dfrac{1}{C_2} + \dfrac{1}{C_3}\right)$$
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> If $C_{eq}$ is the single equivalent capacitance that would store the same charge $Q$ for the same total voltage $V$:
> $$V = \dfrac{Q}{C_{eq}}$$
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> Comparing the two expressions for $V$: …

Q.Derive the formula for equivalent capacitance in series combination.

Concept understanding — Capacitors in Series and Parallel

Q.Derive the formula for equivalent capacitance in series combination.

Concept understanding — Capacitors in Series and Parallel

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