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Two conducting spheres A and B having equal charge Q each placed at large distance are connected with each other as shown. If at t = 0 key (K) is closed, then $(C = 4 π ε_{0} a)$

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Initial current through resistance R is $\frac{Q}{8 π ε_{0} a R}$

Charge on sphere (A) at time t is $Q_{t} = Q + \frac{Q}{3} (1 - e^{- \frac{3 t}{2 C}})$

Total heat dissipated in resistance R is $\frac{4 Q^{2}}{π ε_{0} a}$

Total heat dissipated in resistance R is $\frac{Q^{2}}{4 π ε_{0} a}$

answer is A, B.

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Detailed Solution

$Q_{2 C}^{f} = \frac{2}{3} 2 Q = \frac{4 Q}{3}$

$Q_{2 C}^{f} = \frac{2 Q}{3}$

$\Rightarrow Q_{2 C} = \frac{Q}{3} (1 - e^{- \frac{3 t}{2 C}}) + Q$

$Q_{C} = Q - \frac{Q}{3} (1 - e^{- 3 t / 2 C})$

$I = \frac{Q}{2 C R} = \frac{Q}{8 π \in_{0} a R}$

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