The numerical value of the charge on either plates of capacitor $C$ after a long time t, as shown in the figure is

C E

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\frac{C E R_{1}}{R_{1} + r}

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\frac{C E R_{2}}{R_{2} + r}

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\frac{C E R_{1}}{R_{2} + r}

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Solution

The correct option is C $\frac{C E R_{2}}{R_{2} + r}$
Current flowing in the branch containing capacitor is zero after a long time t.
effective circuit
apply $k v l \Rightarrow i (R_{2} + r) = E$
$i = \frac{E}{R_{2} + r}$
Now P.d accross capacitor $= i \cdot R_{2}$
$v = \frac{E R_{2}}{R_{2} + r}$
We know $Q = c . v$
$Q = \frac{c . E R_{2}}{R_{2} + r}$
$∴ Q = \frac{C E R_{2}}{R_{2} + r}$

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