Question 3: What determines the gradient of a graph of inductive reactance against frequency?

ANSWER

Inductive reactance X_L of an inductor is directly proportional to the frequency of the current flowing in it. Therefore, the graph between inductive reactance and frequency of the current is a straight line. Its slope determines the value of the inductance.

From Ohm’s law applied to the inductors

Here ω = 2πf and f is the frequency of the sinusoidal alternating voltage.

Since 2πL is constant for a particular inductor, therefore,
X_L ∝ f

If a graph is plotted between X_L and f, it would be a straight line and its gradient is given by

Thus gradient of the inductive reactance vs frequency of the current (or voltage) is 2π times the inductance of the inductor. Therefore, the gradient in this case determines the inductance of the inductor.