Question

If the frequency of an AC is made 4 times of its initial value, the inductive reactance will
(A) be 4 times
(B) be 2 times
(C) be half
(D) remain the same

Answer 1

Hint: From the inductive reactance expression, we can determine the inductive reactance variation when the frequency of the alternating current varies. In the expression, the inductive reactance relates directly with the frequency; it means that the inductive reactance is high at a higher frequency.

Complete step by step answer:
In the electric circuits, the current flow is controlled with resistance, so that the desired result and better performance can be obtained by efficient current flow. The resistance tends to stop the current; for the reduction in current flow, we have to increase the resistance and increase the current flow, we have to decrease the current flow. The inductive reactance tends to oppose the current flow in the LRC circuit, and this opposition directly relates to the current frequency. The expression used for the calculation of the inductive reactance is,

${X_L} = 2\pi fL$

Here, ${X_L}$ is the inductive reactance in ohms, $f$ is the frequency of alternating current measured in hertz, $2\pi $ is constant and is the inductance in Henry.

From the above expression, we can write the relation between inductive reactance and frequency as,

${X_c} \propto f$

If the frequency of an AC is made four times its initial value, then from the above relation, the inductive reactance will also become four times from its initial value.
Therefore, if the frequency of an AC is made four times its initial value, the inductive reactance will be four times.

So, the correct answer is “Option A”.

Note:
To remember the inductive reactance expression because, in this solution, we used the expression of the inductive reactance to obtain the relation between inductive reactance and frequency and tell whether the inductive reactance increases or decreases.