Question

An ideal inductor is connected across $220V$ , $50Hz$ and $220V$, $100Hz$ supplies. The current flowing through it in the two cases will be then:

A. Equal

B. Different

C. Zero

D. Infinite

Answer 1

When an inductor is connected through AC voltage source and to find the current through inductor, first find the inductive reactance of the inductor and then use the relation, where voltage is equal to the product of current and inductive reactance of the inductor. And we also know that the reactance of an inductor is dependent on the frequency of input voltage.

Complete step-by-step solution :

Whenever a inductor is connected across a AC voltage source then current though it can be given by the relation:

$V = I{X_L}$

Where:

$V$ is the voltage

$I$ is current through inductor

${X_L}$ is the inductive reactance of the inductor

From above relation:

$I = \dfrac{V}{{{X_L}}}$ --(1)

The formula for reactance of the inductor is:

${X_L} = 2\pi \upsilon L$

Clearly, we can see that the reactance of the inductor depends on the frequency( $\upsilon$ ) of the AC voltage.

Thus, we can say that reactance is directly proportional to the frequency.

${X_L} \propto \upsilon$

And from relation 1 we know that Current is inversely proportional to reactance that means current is inversely proportional to the frequency i.e.

$I \propto \dfrac{1}{\upsilon }$

$I = \dfrac{V}{{2\pi \upsilon L}}$

Now, as given frequencies in the two cases are different then the current flowing through in each case will also be different.

Hence, option (B) is correct.

Note: An ideal inductor has no resistance and only inductance so $R{\text{ }} = {\text{ }}0{\text{ }}\Omega$ and therefore no power is dissipated within the coil. So we can say that an ideal inductor has zero power loss. So, inductors can be defined as passive components as they can both store and deliver energy to the circuit, but they cannot generate energy. An ideal inductor is classed as loss less, meaning that it can store energy indefinitely as no energy is lost.