Question

In an AC generator, a coil with N turns, all of the same area
A and total resistance R, rotates with frequency w in a
magnetic field B. The maximum value of emf generated in
the coil is
(a) N.A.B.R.⍵ (b) N.A.B.
(c) N.A.B.R. (d) N.A.B.⍵

Answer 1

Answer:

Let at time t=0, the coil is vertical and at time t , plane of coil makes an angle θ with the vertical, then

θ=ωt, (ω= uniform angular velocity),

in this position, magnetic flux linked with coil will be,

ϕ=NBAcosθ, (where, A= area of coil,)

or ϕ=NBAcosωt,

now, differentiating this equation w.r.t. time, we get

dt

dϕ

=

dt

d

(NBAcosωt),

or

dt

dϕ

=−NBAωsinωt,

if $e$$ is the emf induced in coil then by Faraday's law,

e=−

dt

dϕ

=NBAωsinωt,

now if, sinωt=1 (maximum),

then e

max

=NBAω,

if ω=1rad/s,

then e

max

=NBA

Answer 2

I think so. answer is N. A. B.