Question

Two capacitor of capacitance $3C$ and $6C$ are charged to potential $V_0$ and $2V_0$ respectively and connected to a resistor of resistance $R$ as shown in fig. Now the both switch $S_1$ and $S_2$ are closed. Find the charge flown in the resistor as a function of time ${}^{\prime }{t}^{\prime }$

• A. $C{V}_0\left(1-e^{-t/9RC}\right)$
• B. $9C{V}_0{e}^{-J/2RC}$
• C. $9C{V}_0{e}^{-t9RC}$
• D. $9C{V}_0\left(1-e^{-t/9RC}\right)$

Answer 1

Answer: (D)

Applying Kirchhoff' law $-\frac{3C{V}_0+q-q_1}{3C}-iR=\mathrm{0...}\left(i\right)$
$\frac{12C{V}_0-q_1}{6C}-iR=\mathrm{0...}\left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$
$q=9C{V}_0\left(1-e^{-U(9RC)}\right)$