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, then the electrical power dissipated would be

Explanation

Current is induced in the short-circuited coil due to the imposed time - varying magnetic field.
Power P = `(e^2)/(R )`
Here e ` = - (dphi)/(dt)` where `phi = NBA`
and `R = (rho l)/(pi r^2) ` where l and r are length and radius of the wire
` therefore P = (pi r^2)/(rho l) [ (d)/(dl) (NBA) ]^2 " or " P = (pi r^2)/(rho l) N^2 A^2 ((dB)/(dt))^2`
or P = (constant) `(N^2r^2)/(l)`
When `r_2 = (r_1)/(2)` then `l_2 = 4l_1`
` P_2/P_1 = ((4N)^2)/(N^2) xx ((r)/(2r))^2 xx ((l)/(4l))`
` therefore P_2/P_1 = (16N^2 xx r^2 xx l)/(N^2 xx 4r^2 xx 4l) " or " P_2/P_1 = 1/1 `
`therefore ` Power dissipated is the same