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Grade 12th passElectromagnetic Induction

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

lalit porwal

8 Years agoGrade 12th pass

1 Answer

Eshan

8 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 becomes $4^2(\dfrac{1}{2})^4=1$ times its initial value. Hence the power dissipated does not change.

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