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  • (i) when an AC 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 AC source. What happens to the brightness of the

(i) when an AC 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 AC 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.

 

 
 
 
 
 

Answers (1)

Let the voltage of ac  source be
V= V_{m}\, \sin \left ( \omega t \right )
The current

I= I_{m}\, \sin \left ( \omega t -\frac{\pi }{2}\right )
Average power 

P_{av}= \frac{\int_{0}^{T}VI\, dt}{T}
T is the time period
\therefore P_{av}= \frac{\int_{0}^{2\pi }V_{m}I_{m}\sin \omega t\sin \left ( \omega t-\frac{\pi }{2} \right )}{2\pi }dt
             = -\frac{1}{2\pi }\int_{0}^{2\pi }V_{m}I_{m}\cos \omega t \sin\omega t\, dt
\left ( \sin \left ( \omega t-\frac{\pi }{2} \right )= -\cos \omega t \right )
P_{av}= -\frac{V_{m}I_{m}}{4\pi }\int_{0}^{2\pi }\sin 2 \omega t
 = 0
ii) when an iron rod is inserted inside the inductor the value of inductance increases \left ( \mu_{iron}> \mu_{air} \right ) There for the current in the circuit decreases, hence the brightness decreases.

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Safeer PP

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