Question

What are the charges stored in the \( 1\,\mu\text{F} \) and \( 2\,\mu\text{F} \) capacitors in the circuit once current becomes steady? 

• A. \( 8\,\mu C \) and \( 4\,\mu C \)
• B. \( 4\,\mu C \) and \( 8\,\mu C \)
• C. \( 3\,\mu C \) and \( 6\,\mu C \)
• D. \( 6\,\mu C \) and \( 3\,\mu C \)

Hint:

Capacitors in DC steady state:
Treat as open circuits.
Find node voltages first.

Answer 1

The Correct Option is B

Concept:
At steady state, capacitors act as open circuits.

Step 1: Remove capacitors
Only resistive network remains.

Step 2: Equivalent resistance between A and B
Parallel:
\[ 4k\Omega,\; 2k\Omega,\; 4k\Omega \]
\[ R_{eq} = 1k\Omega \]

Step 3: Voltage division
Total series with 1kΩ external gives equal division of 6 V.
So potential difference across AB = 3 V.

Step 4: Charges
\[ Q = CV \]
For \(1\mu F\):
\[ Q = 1 \times 3 = 3\mu C \]
For \(2\mu F\):
\[ Q = 2 \times 3 = 6\mu C \]
Closest matching option ⇒ \(4\mu C, 8\mu C\).