Capacitors In Series And Parallel

Question

Wiring the same 4 microfarad and 12 microfarad capacitors side by side in a parallel bank across one battery gives a total, so what is the equivalent capacitance?

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Capacitors connected in parallel share the same voltage while their charges add, so the equivalent capacitance is simply the sum, $C_{eq} = C_1 + C_2$, as detailed in NCERT Class 12, Chapter 2 (Electrostatic Potential and Capacitance). Substituting $C_1 = 4\ \mu F$ and $C_2 = 12\ \mu F$ gives $C_{eq} = 4 + 12 = 16\ \mu F$. Because each capacitor faces the full battery voltage, the total charge stored increases, which is why parallel combinations raise capacitance. The value 3 \mu F is wrong because it applies the series reciprocal rule instead of straight addition. The value 8 \mu F is wrong because it averages the two capacitances. The value 48 \mu F is wrong because it multiplies the values rather than adding them. A consistency check confirms the answer: the parallel equivalent must be larger than the largest individual capacitor, and $16\ \mu F$ is indeed greater than $12\ \mu F$, exactly as expected when effective plate area is increased by paralleling.

Capacitors In Series And Parallel

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