Consider the RC circuit shown in the figure. What will be the final charge Q∞ and the equivalent time constant of the circuit.

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Consider the RC circuit shown in the figure. What will be the final charge $Q_{\infty}$ and the equivalent time constant of the circuit.

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$Q = CE / 3$

$τ = 4 R C / 3$

$Q = C E / 2$

$τ = R C$

answer is B, D.

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Detailed Solution

In steady state, current through each branch is $\frac{E}{3 R} .$ The final potential difference across the capacitor is $(\frac{E}{3 R} . 2 R - \frac{E}{3 R} . R) i . e . \frac{E}{3} .$ $E / 3 . So Q = C E / 3$

$R_{eff} = 4 R / 3 \Rightarrow τ = R_{e f f} \times C = 4 R C / 3$

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