In a DC circuit, after a long time, what is the effective resistance of an ideal capacitor, and does it conduct current?

In a DC circuit, after a long time, what is the effective resistance of an ideal capacitor, and does it conduct current?

• A. Infinite resistance; no steady-state current
• B. Zero resistance; continuous current
• C. Finite resistance; some current
• D. Negative resistance; reverse current

Answer: (C)

In DC steady state, a capacitor stops conducting current. Once it has charged, the voltage across it is constant, so the current through it is i = C dv/dt, and with dv/dt = 0, the current is zero. This means its impedance to DC is effectively infinite (Z = 1/(jωC) with ω = 0 gives infinite impedance), so the capacitor presents infinite resistance and carries no steady current. Only during the charging phase is there a transient current; afterward, it behaves as an open circuit.

In DC steady state, a capacitor stops conducting current. Once it has charged, the voltage across it is constant, so the current through it is i = C dv/dt, and with dv/dt = 0, the current is zero. This means its impedance to DC is effectively infinite (Z = 1/(jωC) with ω = 0 gives infinite impedance), so the capacitor presents infinite resistance and carries no steady current. Only during the charging phase is there a transient current; afterward, it behaves as an open circuit.