Q. 4

# An inductor-coil having some resistance is connected to an AC source. Which of the following quantities have zero average value over a cycle?

A. Current

B. Induced emf in the inductor

C. Joule heat

D. Magnetic energy stored in the inductor.

Answer :

For an inductor-coil circuit with some resistance, the current and the induced emf in the inductor are of the sinusoidal form. It is shown in the diagram below:

Here, T is the time period.

From the graph, we can see that the average value of current or induced emf over a cycle is 0.

Mathematically, we can see it in the following way:

Let the emf be of the form E = E_{0}sinωt, where E_{0} = peak value of emf, ω = angular frequency, t = time.

Average emf over an entire cycle

Where T = time period

Similarly, we can also show that the average value of current over a full time period is also 0.

Hence, options (A) and (B) are correct.

Joule heat is given by H = i_{rms}^{2} x R, where i_{rms} = rms value of current, and R = resistance, which is non zero. Hence, option (C) is incorrect.

Magnetic energy stored in inductor is given by , where L = inductance, i_{rms} = rms value of current, which is non zero. Hence, option (D) is incorrect.

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