(a) Calculate the inductive reactance of a 3.00 mH inductor when 60.0 Hz and 10.0 kHz AC voltages are applied. (b) What is the rms current at each frequency if the applied rms voltage is 120 V?
Strategy
The inductive reactance is found directly from the expression X_{L}=2 \pi f L . 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.
Solution for (a)
Entering the frequency and inductance into Equation X_{L}=2 \pi f L gives
X_{L}=2 \pi f L=6.28(60.0 / s )(3.00 mH )=1.13 \Omega \text { at } 60 Hz. (23.53)
Similarly, at 10 kHz,
X_{L}=2 \pi f L=6.28\left(1.00 \times 10^{4} / s \right)(3.00 mH )=188 \Omega \text { at } 10 kHz. (23.54)
Solution for (b)
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
I=\frac{V}{X_{L}}=\frac{120 V }{1.13 \Omega}=106 A \text { at } 60 Hz. (23.55)
Similarly, at 10 kHz,
I=\frac{V}{X_{L}}=\frac{120 V }{188 \Omega}=0.637 A \text { at } 10 kHz. (23.56)
Discussion
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.