When an a.c. source is connected to an ideal inductor show that the average power supplied by the source over a complete cycle is zero

CBSE Class 12 CBSE Class 12 Physics
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(i) When an a.c. source is connected to an ideal inductor show 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

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(ii) When an iron rod is inserted into the inductor, the self-inductance of the inductor will increase in the potential drop across the inductor and a subsequent decrease in the voltage across the bulb, therefore, resulting in the bulb to go dim.