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Potential Energy of a System of Multiple Point Charges

Three uncharg...

Question

Three uncharged capacitors of capacitance $C_{1}, C_{2}$ and $C_{3}$ are connected to one another as shown in figure. The potential at O will be :

3 V

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\frac{49}{11} V

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4 V

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\frac{3}{11} V

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Solution

The correct option is A $\frac{49}{11} V$
As the capacitors are uncharged so total charge of system is zero. i.e,
$q_{1} + q_{2} + q_{3} = 0$
or $C_{1} (V_{1} - V_{O}) + C_{2} (V_{2} - V_{O}) + C_{3} (V_{3} - V_{O}) = 0$
or $60 (6 - V_{O}) + 20 (2 - V_{O}) + 30 (3 - V_{O}) = 0$
or $36 - 6 V_{O} + 4 - 2 V_{O} + 9 - 3 V_{O} = 0$
or $11 V_{O} = 49 \Rightarrow V_{O} = \frac{49}{11} V$

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