Question

In an AC generator, a coil with $N$ turns, all of the same area $A$ and total resistance $R$, rotates with frequency in a magnetic field $B$. The maximum value of emf generated in the coil is:

• A. $N.A.B$
• B. $N.A.B.R$
• C. $\frac{1}{10}N.A.B$
• D. $\frac{1}{10}N.A.B.R$

Answer 1

The correct option is A $N.A.B$

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

$\theta =\omega t$, ($\omega =$ uniform angular velocity),

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

$\varphi =NBA\cos \theta$, (where, $A=$ area of coil,)

or $\varphi =NBA\cos \omega t$,

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

$\frac{d\varphi }{dt}=\frac{d}{dt}\left(NBA\cos \omega t\right)$,

or $\frac{d\varphi }{dt}=-NBA\omega \sin \omega t$,

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

$e=-\frac{d\varphi }{dt}=NBA\omega \sin \omega t$,

now if, $\sin \omega t=1$ (maximum),

then $e_{max}=NBA\omega$,

if $\omega =1rad/s$,

then $e_{max}=NBA$