Question 4: How does doubling the frequency affect the reactance of (a) inductor (b) capacitor?

• ### Doubling the frequency doubles the inductive reactance

Doubling the frequency of alternating current will also double the inductive reactance.

Let an A.C source is connected across the ends of an inductor, then apply Ohm’s law,

Let we double the frequency of the source so that the new frequency f is equal to 2f. Therefore the new reactance is

Here we have substituted the value of XL from equation (B).

Thus when we double the frequency of the current, the inductive reactance is also doubled.

(b)

### Capacitive reactance becomes half when frequency is doubled

Unlike inductive reactance, the capacitive reactance becomes half when the frequency of the A.C source is doubled. Let a source of alternating current is connected across a capacitor. Apply Ohm’s law

Now let the frequency of A.C source is doubled and the new frequency is f1 = 2f. Let the new reactance of the capacitor is Xc1. Then put them in equation (Y).

Here the value of XC is substituted from equation (Y).

Equation (Z) shows the capacitive reactance is halved when the frequency of the current doubles.