Three capacitors each of capacitance 9 pF are connected in series. (a) What is the total capacit

step 1 This question belongs to the capacitance in which we have three capacitors, each of capacitance

Three capacitors each of capacitance 9 pF are connected in...

Three capacitors each of capacitance $9 \mathrm{pF}$ are connected in series.
(a) What is the total capacitance of the combination?
(b) What is the potential difference across each capacitor if the combination is connected to a $120 \mathrm{~V}$ supply?

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Key Concepts

Series Combination of Capacitors

When capacitors are connected in series, the same charge accumulates on each capacitor, but the voltage across each capacitor can differ. The overall effect is that the total voltage across the series configuration is the sum of the individual voltage drops, while the stored charge remains constant throughout the series circuit.

Equivalent Capacitance

For capacitors connected in series, the equivalent capacitance is found using the reciprocal formula: 1/C_eq = 1/C1 + 1/C2 + ... + 1/Cn. This means that the total capacitance is less than any individual capacitor's capacitance, highlighting the reduction in energy storage capability when capacitors are arranged in a series configuration.

Voltage Division in Series Capacitors

In a series circuit, the supply voltage divides among the capacitors according to their capacitances. When the capacitors have equal capacitance, the voltage is distributed equally across each capacitor. In general, the voltage drop across any capacitor in a series is inversely proportional to its capacitance, ensuring that the sum of the individual voltage drops equals the total applied voltage.

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