alternating-currents Question 20
Question: Q. 5. (i) When an $a c$ source is connected to an ideal inductor shows that the average power supplied by the source over a complete cycle is zero.
(ii) A lamp is connected in series with an inductor and an $a c$ source. What happens to the brightness of the lamp when the key is plugged in and an iron rod is inserted inside the inductor? Explain.
U] [O.D. I, II, III 2016]
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Solution:
Ans. (i)
$$ P_{a v}=I_{a v} \times V_{a v} \cos \phi $$
For an ideal inductor, $\phi=\frac{\pi}{2}$
$$ \begin{align*} \therefore \quad & P_{a v}=I_{a v} \times V_{a v} \cos \frac{\pi}{2} \ & P_{a v}=0 \end{align*} $$
$1 / 2$
(ii) Brightness decreases. Because as iron rod is inserted, inductance increases, hence the current will decrease with decrease in brightness.
Detailed Answer :
(i) The average power supplied by the source over a complete cycle is
$$ P_{a v}=E_{r m s} \times I_{r m s} \times \cos \phi $$
When the circuit carries an ideal inductor, then the phase difference between the current and voltage is $\pi$ $\overline{2}$
In case of pure inductive circuit, $\phi=\frac{\pi}{2} \Rightarrow \cos \frac{\pi}{2}=0$ So power dissipated $=0$
Hence, when an ac source is connected to an ideal inductor, the average power supplied by the source over a complete cycleis zero.
[CBSE Marking Scheme 2016]
AI Q. 6. An inductor $L$ of inductance $X_{L}$ is connected in series with a bulb $B$ and an $a c$ source. How would brightness of the bulb change when (i) number of turns in the inductor is reduced, (ii) an iron rod is inserted in the inductor and (iii) a capacitor of reactance $X_{C}=X_{L}$ is inserted in series in the circuit. Justify your answer in each case.
U] [Delhi I, II, III 2015]
