Question

A galvanometer (G) of $2 \, \Omega$ resistance is connected in the given circuit. The ratio of charge stored in $C_1$ and $C_2$ is:

• A. \(\frac{2}{3}\)
• B. \(\frac{3}{2}\)
• C. 1
• D. \(\frac{1}{2}\)

Answer 1

The Correct Option is D

Given:

In steady state, we have: \[ R_{\text{eq}} = 12 \, \Omega \]

Step 1: Calculating the current:

The current \( I \) is given by: \[ I = \frac{6}{12} = 0.5 \, \text{A} \]

Step 2: Potential difference across capacitors:

The potential difference across capacitor \( C_1 \) is: \[ V_{C_1} = 3 \, \text{V} \] The potential difference across capacitor \( C_2 \) is: \[ V_{C_2} = 4 \, \text{V} \]

Step 3: Calculating the charge on the capacitors:

The charge on \( C_1 \) is: \[ q_1 = C_1 V_1 = 12 \, \mu C \] The charge on \( C_2 \) is: \[ q_2 = C_2 V_2 = 24 \, \mu C \]

Step 4: Ratio of the charges:

The ratio of the charges is: \[ \frac{q_1}{q_2} = \frac{1}{2} \]