In DC steady-state, the impedance of an inductor as angular frequency ω approaches zero is what value?

In DC steady-state, the impedance of an inductor as angular frequency ω approaches zero is what value?

• A. 0 Ω
• B. ∞
• C. 1 Ω
• D. Not defined

Answer: (A)

In DC steady-state, the angular frequency is zero, so the inductor’s impedance Z_L = j ω L becomes zero. This means an ideal inductor behaves like a short circuit for constant current: the current can flow freely and the voltage across the inductor drops to zero in steady state. That’s why the DC impedance is 0 Ω. The other options don’t fit because the impedance of an inductor does not diverge at zero frequency, nor does it take a nonzero fixed value like 1 Ω; and with an ideal model there’s no undefined impedance at ω = 0. If you considered a real coil, its DC impedance would be the winding resistance, but in the ideal case it’s zero.

In DC steady-state, the angular frequency is zero, so the inductor’s impedance Z_L = j ω L becomes zero. This means an ideal inductor behaves like a short circuit for constant current: the current can flow freely and the voltage across the inductor drops to zero in steady state. That’s why the DC impedance is 0 Ω. The other options don’t fit because the impedance of an inductor does not diverge at zero frequency, nor does it take a nonzero fixed value like 1 Ω; and with an ideal model there’s no undefined impedance at ω = 0. If you considered a real coil, its DC impedance would be the winding resistance, but in the ideal case it’s zero.