Question

What is the power dissipated by an ideal inductor in ac circuit? Explain.

Answer 1

Solving this we need to know the formula of power and of how an inductor dissipates power in an ac circuit. We have to understand the concept of phase difference between voltage and current and how it is related to in different circuits with the components of resistor, inductor and capacitor.

Complete step by step solution:
In case of an AC circuit, we know that the formula for power P is as follows:
P = ${V_{rms}}{I_{rms}}\cos \phi$ , where the terms are rms value of voltage, current and the cosine of phase difference between voltage and current respectively.
To understand the phase difference in case of inductors let us understand its application: Inductors work by storing energy in the form of a magnetic field which is created when s voltage is applied across terminals of the inductor. Now the growth of the current in the inductor is not instantaneous but it is determined by the back emf of the inductor. Thus, there is a phase difference between the voltage and current, that is, current lags voltage by an angle of ${90^{^o}}$.
Thus, we get the value of cosine of phase angle as zero. Hence the total power dissipated by an ideal inductor in ac circuit is zero.
Now to understand this we can use another concept:
In an ideal inductor there is no resistive component, thus R = $0$.
Now, cosine ($\cos \phi$ ) = $\dfrac{R}{Z}$
Now as R is zero, thus$\cos \phi$ is zero.
Thus P = ${V_{rms}}{I_{rms}}\cos \phi$ = ${V_{rms}}{I_{rms}} \times 0$= $0$.
Thus, the power dissipated by an ideal inductor in an ac circuit is zero.

Note: We need to know the phase relations for different components in an AC circuit and use the formula for power. Most of the time we get confused when current lags voltage and when voltage lags current, thus we need to remember this by reading the concepts. We can get questions including all the components; thus, we need to read the formulas of an AC circuit.