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

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 X_{L} 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 f_{1} = 2f. Let the new reactance of the capacitor is X_{c1}. Then put them in equation (Y).
Here the value of X_{C} is substituted from equation (Y).
Equation (Z) shows the capacitive reactance is halved when the frequency of the current doubles.
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