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

Options

A. halved
B. the same
C. doubled
D. quadrupled

Answer

D

Explanation

`phi=NBA`
`e=(dphi)/(dt)=N(dB)/(dt)A`
Power dissipated `P=(e^(2))/(R) implies PpropN^(2)`
When no. of turn quadrupled, emf becomes `16` times.
When radius of cross-section of wire reduced to half,
resistance becomes `4` times.
`p'=(16e^(2))/(4R)=(4e^(2))/(R)=4P` .