A 1 μ F capacitor is connected in the circuit shown. The emf of the cell is 3 volts and internal resistance is 0.5 ohm. The resistances R 1 and R 2 have values 4 ohm and 1 ohm respectively. The ch

Question

A 1 μ F capacitor is connected in the circuit shown. The emf of the cell is 3 volts and internal resistance is 0.5 ohm. The resistances R 1 ​ and R 2 ​ have values 4 ohm and 1 ohm respectively. The charge on the capacitor in steady state must be:

TestHub · Accepted Answer

In steady state the current in the branch containing the capacitor is zero, so the emf $E$ is shared between $r$ and $R_{2}$ in the ratio of their resistances.
Voltage across $R_{2}$ :
$\frac{E R _{2}}{R _{2} + r} = 2$ V = voltage across capacitor
$Q = C V_{C} = 1 μ$ F $\times 2$ V $= 2 μ$ C

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