Calculating Inductive Reactance and then Current

The inductive reactance is found directly from the expression $X_L=\mathrm{2\pi }\text{fL}$. Once $X_L$ has been found at each frequency, Ohm’s law as stated in the Equation $I=V/X_L$ can be used to find the current at each frequency.

Entering the frequency and inductance into Equation $X_L=\mathrm{2\pi }\text{fL}$ gives

Similarly, at 10 kHz,

The rms current is now found using the version of Ohm’s law in Equation $I=V/X_L$, given the applied rms voltage is 120 V. For the first frequency, this yields

Similarly, at 10 kHz,

The inductor reacts very differently at the two different frequencies. At the higher frequency, its reactance is large and the current is small, consistent with how an inductor impedes rapid change. Thus high frequencies are impeded the most. Inductors can be used to filter out high frequencies; for example, a large inductor can be put in series with a sound reproduction system or in series with your home computer to reduce high-frequency sound output from your speakers or high-frequency power spikes into your computer.