Question

The charge stored by the capacitor C in the given circuit in the steady state is _________ $\mu$C.

• A. 10
• B. 7.5
• C. 5
• D. 12.5

Hint:

In steady state, treat the capacitor as an open circuit. Calculate the potential at its terminals by treating the remaining circuit as purely resistive.

Answer 1

The Correct Option is C

We are required to find the charge stored by the capacitor when the circuit reaches steady state.

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Given:

• Capacitance: \[ C = 5~\mu\text{F} = 5 \times 10^{-6}~\text{F} \]
• Voltage across the capacitor at steady state: \[ V = 1~\text{V} \]

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Key Concept:

In steady state (DC conditions), a capacitor behaves as an open circuit and charges to the voltage across its terminals.

The charge stored in a capacitor is given by:

\[ Q = C V \]

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Calculation:

\[ Q = (5 \times 10^{-6})(1) = 5 \times 10^{-6}~\text{C} \]

\[ Q = 5~\mu\text{C} \]

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Final Answer:

\(\boxed{5~\mu\text{C}}\)