Three capacitors each of capacitance 9 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 V supply?
(a) Capacitance of each of the three capacitors, C = 9 pF
Equivalent capacitance (C’) of the combination of the capacitors is given by the relation,
$\frac{1}{C^{\prime}}=\frac{1}{C}+\frac{1}{C}+\frac{1}{C}$
$\Rightarrow \frac{1}{C^{\prime}}=\frac{1}{9}+\frac{1}{9}+\frac{1}{9}=\frac{1}{3}$
$\Rightarrow C^{\prime}=3 \mathrm{pF}$
Therefore, total capacitance of the combination is
(b) Supply voltage, V = 120 V
Potential difference (V') across each capacitor is equal to one-third of the supply voltage.
$\therefore V^{\prime}=\frac{V}{3}=\frac{120}{3}=40 \mathrm{~V}$
Therefore, the potential difference across each capacitor is 40 V.
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