NEIEP Electrical Theory and Application (430) Practice Exam

Inductive reactance shows how an inductor resists changes in current in an AC circuit, and it grows as the current changes more rapidly with frequency. For an inductor L, the voltage across it is V = L di/dt. If the current is sinusoidal, i = I sin(ωt), then di/dt = ωI cos(ωt), so the voltage has magnitude V = ωLI. The inductive reactance is the ratio V/I, giving XL = ωL. Since ω = 2πf, XL = 2πfL, which means XL increases as frequency increases. For example, doubling the frequency doubles XL for the same L.

The other possibilities aren’t correct for inductive reactance: a capacitor’s reactance is Xc = 1/(ωC) and decreases with frequency; XL = 1/(ωL) would be the reciprocal of the correct expression; and R × ω would imply a frequency-dependent resistance, not the inductive reactance of an ideal inductor.