### Video Transcript

At what frequency is the reactance of a 20-microfarad capacitor equal to that of a 10-millihenry inductor?

We can call our 20-microfarad value capital πΆ and our 10-millihenry inductor capital πΏ. We want to solve for the frequency at which the reactance of these two elements is equal. Weβll call that frequency π.

We can begin by recalling the mathematical relationships for the reactance of a capacitor and for an inductor. We recall that reactance is a measure of how much the flow of current is resisted. Itβs like resistance and even has units of ohms.

The reactance of a capacitor is defined as one over two π times the frequency π multiplied by the capacitance πΆ. And the reactance for an inductor is equal to two ππ times the inductance πΏ. Notice that both reactance terms involve the angular frequency π.

In our exercise, we want to solve for frequency π when the reactance of the capacitor is equal to the reactance of the inductor. So when one over two πππΆ is equal to two πππΏ, we want to know what is π.

When we rearrange this equation algebraically to solve for π, we find itβs equal to one over two π times the square root of πΏπΆ. Since πΏ and πΆ are both given in the problem statement, we can plug in those values now to solve for π.

When we do, making sure to express our inductance in units of henries and our capacitance in units of farads, when we enter these values on our calculator, we find that, to two significant figures, π is 360 hertz. Thatβs the frequency at which the reactance of the capacitor equals the reactance of the inductor.