In the given circuit, the capacitor has capacitance $C$ and it is filled with a resistive material of effective resistance $r$ . The switch S is closed at time $t = 0$ . The charge on capacitor as a function of time $t$ is

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$\frac{CEr}{(R + r)} (1- e^{- \frac{t}{τ}}), τ = (R + r) C$

$CE (1- e^{- \frac{t}{τ}}), τ = (R + r) C$

$\frac{CEr}{(R + r)} (1- e^{- \frac{t}{τ}}), τ = \frac{CRr}{(R + r)}$

$EC (1- e^{- \frac{t}{τ}}), τ = \frac{CrR}{(R + r)}$

answer is C.

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Detailed Solution

$V_{\max} = E (\frac{r}{R + r})$

$∴ q_{\max} = \frac{ECr}{(R + r)}$
$τ = \frac{CrR}{(R + r)}$

$∴ q = \frac{ECr}{(R + r)} (1 - e^{\frac{- t}{τ}})$

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