(a) Draw a labelled diagram of a.c. generator. Derive the expression for the instantaneous value of the emf induced in the coil.
(b) A circular coil of cross-sectional area `200 cm^(2)` and 20 turns is rotated about the vertical diameter with angular speed of 50 rad `s^(-1)` in a uniform magnetic field of magnitude `3.0 xx 10^(-2)T`.
Calculate the maximum value of the current in the coil.

Explanation

(a) See Short Answer Question Number 53.
(b) Here cross-sectional area `A = 200 cm^(2) = 200 xx 10^(-4)m^(2)`, number of turns N = 20, angular speed `omega = 50 "rad s"^(-1)` and magnetic field `B = 3.0 xx 10^(-2)T`.
`therefore` Maximum value of the induced emf `varepsilon_(m) = NABomega = 20 xx (200 xx 10^(-4))xx(3.0 xx10^(-2))xx50 = 0.6 V`.
If R be the resistance of the coil then maximum value of the current `(I_(m))` flowing in the coil is given as :
`I_(m) = (varepsilon_(m))/R=(0.6)RA`