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Initially, capacitors C₁, and C₂, carry a charge of 300 $μ C$ and 360 $μ C$ , respectively, with polarities as shown in the figure, while capacitor C₃ is uncharged.
After switch S is closed, steady state charge on C₃is:

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100 $μ C$

120 $μ C$

180 $μ C$

210 $μ C$

answer is D.

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Detailed Solution

The initial charges on the two capacitors are $q_{1} = 300 μ C$ and $q_{2} = 360 μ C$

Let steady state charge distribution be as shown in the figure.

Writing loop equations, we have

$\begin{array}{l} \frac{q_{1} - q}{3} - \frac{q}{2} + \frac{q_{2} - q}{2} = 0 \\ \Rightarrow 2 (q_{1} - q) - 3 q + 3 (q_{2} - q) = 0 \\ \Rightarrow q = \frac{2 q_{1} + 3 q_{2}}{8} = 210 μ C \end{array}$

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