A coil of number of turns N, area A, is rotated at a constant angular speed `omega`, in a uniform magnetic field B, and connected to a resistor R. Deduce expressions for :
(i) maximum emf induced in the coil, (ii) power dissipated in the coil.

Explanation

(i) As shown in Short Answer Question Number 14, induced emf
`varepsilon = NBA omega sin omegat.`
`therefore` Maximum emf induced in the coil
`varepsilon_(max) = N B A omega` [when `sin omegat = 1]`
(ii) Istantaneous power dissipation in the coil Pinsi `P_(inst).= varepsilon_(2)/R = (N^(2)B^(2)A^(2)omega^(2))/R sin^(2)omegat`
For one complete cycle mean value of `sin^(2) omegat =1/2`. Hence, the mean value of power dissipation in the coil is given by
`P("average") = (N^(2) B^2)A^(2) omega^(2))/R.(1/2)=(N^(2)B^(2)A^(2)omega^(2))/(2R)`.