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?
What are the charges stored in the \( 1\,\mu\text{F} \) and \( 2\,\mu\text{F} \) capacitors in the circuit once current becomes steady?
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Capacitors in DC steady state:
Treat as open circuits.
Find node voltages first.
Treat as open circuits.
Find node voltages first.
Updated On: Apr 9, 2026
- \( 8\,\mu C \) and \( 4\,\mu C \)
- \( 4\,\mu C \) and \( 8\,\mu C \)
- \( 3\,\mu C \) and \( 6\,\mu C \)
- \( 6\,\mu C \) and \( 3\,\mu C \)
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The Correct Option is B
Solution and Explanation
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 ⇒ \(4\mu C, 8\mu C\).
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 ⇒ \(4\mu C, 8\mu C\).
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