Why does an inductor act as a short circuit in a direct current (DC) circuit after a long time?

Why does an inductor act as a short circuit in a direct current (DC) circuit after a long time?

• A. The impedance becomes zero because ω approaches 0 for DC, so jωL=0.
• B. The energy stored in the magnetic field prevents current from changing.
• C. It blocks DC and behaves as an open circuit.
• D. The inductance increases indefinitely, blocking current.

Answer: (A)

In DC steady state, an inductor acts like a short circuit because its impedance to a constant current is zero. The impedance of an inductor is Z_L = jωL, and direct current has angular frequency ω = 0, so Z_L = 0. This means there’s no voltage drop across an ideal inductor once the current has settled, and current flows through as if through a plain wire. The underlying reason is that an inductor resists changes in current: when you first apply the DC source, di/dt is nonzero and the inductor develops a voltage v_L = L di/dt to oppose the change. As time passes and di/dt goes to zero, that voltage disappears and the current becomes constant. In real inductors there’s usually a small series resistance, so it isn’t a perfect short, but in the ideal model its DC impedance is effectively zero after a long time.

In DC steady state, an inductor acts like a short circuit because its impedance to a constant current is zero. The impedance of an inductor is Z_L = jωL, and direct current has angular frequency ω = 0, so Z_L = 0. This means there’s no voltage drop across an ideal inductor once the current has settled, and current flows through as if through a plain wire. The underlying reason is that an inductor resists changes in current: when you first apply the DC source, di/dt is nonzero and the inductor develops a voltage v_L = L di/dt to oppose the change. As time passes and di/dt goes to zero, that voltage disappears and the current becomes constant. In real inductors there’s usually a small series resistance, so it isn’t a perfect short, but in the ideal model its DC impedance is effectively zero after a long time.