In steady-state DC analysis, what is the typical behavior of an inductor and of a capacitor?

In steady-state DC analysis, what is the typical behavior of an inductor and of a capacitor?

• A. The inductor acts as a short circuit and the capacitor acts as an open circuit.
• B. The inductor acts as an open circuit and the capacitor acts as a short circuit.
• C. Both are open circuits.
• D. Both are short circuits.

Answer: (A)

In steady-state direct current, an inductor and a capacitor behave differently due to how they store energy and respond to constant currents. An ideal inductor presents almost no opposition to a constant current because its impedance is Z_L = jωL, and when the frequency is zero (DC), ω = 0, so Z_L = 0. That makes it act like a short circuit, letting DC flow through with essentially no voltage drop across it. A capacitor, by contrast, charges up when a DC voltage is applied and then blocks further DC current. Its impedance is Z_C = 1/(jωC); at DC, ω = 0, so Z_C tends toward infinity, which is an open circuit. The capacitor stores charge and maintains a fixed voltage, preventing continuous current flow. In real circuits there can be small resistive leakage in capacitors and series resistance in inductors, so they aren’t perfect shorts or opens, but the ideal behavior in steady-state DC is exactly that: the inductor behaves as a short, and the capacitor behaves as an open.

In steady-state direct current, an inductor and a capacitor behave differently due to how they store energy and respond to constant currents. An ideal inductor presents almost no opposition to a constant current because its impedance is Z_L = jωL, and when the frequency is zero (DC), ω = 0, so Z_L = 0. That makes it act like a short circuit, letting DC flow through with essentially no voltage drop across it.

A capacitor, by contrast, charges up when a DC voltage is applied and then blocks further DC current. Its impedance is Z_C = 1/(jωC); at DC, ω = 0, so Z_C tends toward infinity, which is an open circuit. The capacitor stores charge and maintains a fixed voltage, preventing continuous current flow.

In real circuits there can be small resistive leakage in capacitors and series resistance in inductors, so they aren’t perfect shorts or opens, but the ideal behavior in steady-state DC is exactly that: the inductor behaves as a short, and the capacitor behaves as an open.