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  • A coil is placed in a time-varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in

A coil is placed in a time-varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be :

(Assume the coil to be short circuited.)

Option: 1

Halved


Option: 2

Quadrupled


Option: 3

The same


Option: 4

Doubled


Answers (1)

best_answer

using Faradays law
\epsilon =\left|-\frac{d \phi}{d t}\right|=N \frac{d B }{d t}A
 As \ N \ \text{is half} \Rightarrow \epsilon'=\frac{\epsilon }{2}

Now wire of length l  was forming  N loops 

 As \ N \ \text{is half} \Rightarrow l'=\frac{l}{2}
So overall for wire its length is halved &  radius is doubled
\begin{aligned} &R=\frac{\rho l}{\pi r^{2}} \\ &R^{\prime}=R / 8 \\ &P_{I}=\epsilon ^{2}/ R \\ &P_{f}=\frac{(\epsilon /2)^{2}}{(R/8)}=\frac{2 \varepsilon^{2}}{R}=2 P_{I} \end{aligned}

Hence option 4 (D) is correct

Posted by

manish painkra

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