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 $'t'$

• A. $CV_{0}\left(1 - e^{- t / 9 R C}\right)$
• B. $9CV_{0}e^{- J / 2 R C}$
• C. $9CV_{0}e^{- t 9 R C}$
• D. $9CV_{0}\left(1 - e^{- t / 9 R C}\right)$

Answer 1

Answer: (D)

Applying Kirchhoff' law $-\frac{3 C V_{0} + q - q_{1}}{3 C}-iR=0...\left(i\right)$
$\frac{12 C V_{0} - q_{1}}{6 C}-iR=0...\left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$
$q=9CV_{0}\left(1 - e^{- U \left(\right. 9 R C \left.\right)}\right)$