Question

If the rotational velocity of a dynamo armature is doubled, then the induced e.m.f. will become

• A. half
• B. two times
• C. four times
• D. unchanged

Answer 1

Answer: (B)

If $A$ is the area of the coil, there are $N$ turns in the coil, $\omega$ being the angular velocity of the armature, then the flux through each turn in time $t$ is given by
$\varphi =BA\cos \omega t$
Using Faraday's Law, the emf induced in each turn of the coil is
$-\frac{d\varphi }{dt}=BA\omega \sin \omega t$
The total induced emf in the coil
$\epsilon =NBA\omega \sin \omega t$
Now if we double $\omega ,\epsilon$ will be doubled.