Two capacitors A and B having capacitances 10 μF and 20 μF are connected in series with a 12 V

step 1 According to question, two capacitors A and B, two capacitors, capacitor A and capacitor B are c

Two capacitors A and B having capacitances 10 μF and 20 μF...

Two capacitors $A$ and $B$ having capacitances $10 \mu \mathrm{F}$ and $20 \mu \mathrm{F}$ are connected in series with a $12 \mathrm{~V}$ battery. The ratio of the charges on $A$ and $B$ is :
(a) $0.5: 1$
(b) $1: 1$
(c) $2: 1$
(d) $2: 4$

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Key Concepts

Equivalent Capacitance in Series

The overall or equivalent capacitance of capacitors connected in series is found by taking the reciprocal of the sum of the reciprocals of the individual capacitances. This equivalent capacitance is always lower than the smallest individual capacitor in the series.

Voltage Division in Series

When capacitors are arranged in series, the applied voltage from the battery is divided among them, with each capacitor developing a voltage proportional to the inverse of its capacitance. Despite different voltage drops, the charge remains the same across all capacitors.

Capacitors in Series

In a series configuration, capacitors are connected end-to-end so that the same charge flows through each capacitor. This means that no matter how the individual capacitances differ, every capacitor in the series holds an identical amount of charge.

Capacitance

Capacitance is a measure of a capacitor's ability to store charge per unit voltage. It is determined by physical characteristics like the plate area, separation distance, and the dielectric material between the plates.

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