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a short circuited is placed in atime varying magnetic field. electrical power is dissipated due to the current induced in the coil. if the no of turns were to be quadrupled & the wire radius halved the electrical power dissipated would be

a short circuited is placed in atime varying magnetic field. electrical power is dissipated due to the current induced in the coil. if the no of turns were   to be quadrupled & the wire radius halved the electrical power dissipated would be

Grade:12th pass

1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
Dear student,

The emf induced in the coil=-\dfrac{d\phi}{dt}=-NA\dfrac{dB}{dt}=-N\pi r^2\dfrac{dB}{dt}\propto Nr^2
Hence power dissipated in the coil=i^2R=\dfrac{EMF^2}{R}\propto EMF^2\propto N^2r^4
Hence when number of turns is quadrupled and radius halved, the power becomes4^2(\dfrac{1}{2})^4=1times its initial value. Hence the power dissipated does not change.

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