What value of inductance should be used if a $20.0\text{ k}\Omega$ reactance is needed at a frequency of 500 Hz?

Video Transcript

This is College Physics Answers with Shaun Dychko. With an inductive reactance of 20.0 kiloohms, which is 20.0 times 10 to the 3 ohms and a frequency of 500 hertz, what inductance should we have? So the inductive reactance is 2π times frequency times inductance and we can solve for L by dividing both sides by 2πf. So the inductance then is the reactance— 20.0 times 10 to the 3 ohms— divided by 2π times the frequency of 500 hertz, which is 6.37 henries.