Which statement about a capacitor in a DC circuit after a long time is true?

Which statement about a capacitor in a DC circuit after a long time is true?

• A. It behaves as an open circuit
• B. It behaves as a short circuit
• C. It behaves as a constant current source
• D. It blocks AC and DC has no effect

Answer: (A)

In DC steady state, a capacitor ends up charged and no current flows through it. This follows from i = C dv/dt: with a constant DC voltage, dv/dt = 0, so i = 0. Because the branch containing the capacitor carries no current, it behaves like an open circuit to the rest of the circuit. The capacitor’s voltage settles to the DC source value (or to the final node voltage dictated by the circuit) and remains there as long as the DC conditions stay constant. That’s why the statement describing it as an open circuit best captures its long-time behavior. Why the other ideas aren’t correct: it doesn’t act as a short circuit, since a short would require continuous current through the element. It isn’t a constant current source, because the current through a capacitor under DC becomes zero once steady state is reached. And while a capacitor blocks steady DC current, DC does affect the capacitor during charging by establishing its final voltage, so the claim that DC has no effect is inaccurate.

In DC steady state, a capacitor ends up charged and no current flows through it. This follows from i = C dv/dt: with a constant DC voltage, dv/dt = 0, so i = 0. Because the branch containing the capacitor carries no current, it behaves like an open circuit to the rest of the circuit.

The capacitor’s voltage settles to the DC source value (or to the final node voltage dictated by the circuit) and remains there as long as the DC conditions stay constant. That’s why the statement describing it as an open circuit best captures its long-time behavior.

Why the other ideas aren’t correct: it doesn’t act as a short circuit, since a short would require continuous current through the element. It isn’t a constant current source, because the current through a capacitor under DC becomes zero once steady state is reached. And while a capacitor blocks steady DC current, DC does affect the capacitor during charging by establishing its final voltage, so the claim that DC has no effect is inaccurate.