Question

If the rotational velocity of dynamo armature is four times, then the induced emf of the dynamo will be :-

• A. Four times
• B. Eight times
• C. Half
• D. None of these

Answer 1

Answer: (A)

Four times

Answer 2

The induced electromotive force (EMF) in a dynamo (AC generator) is given by the formula:

$E = E_0 \sin(\omega t)$

where the peak induced EMF $E_0$ is given by:

$E_0 = NBA\omega$

Here,

$N$ = number of turns in the coil

$B$ = magnetic field strength

$A$ = area of the coil

$\omega$ = angular velocity (rotational velocity)

From the formula $E_0 = NBA\omega$, it is clear that the peak induced EMF ($E_0$) is directly proportional to the angular velocity ($\omega$).

$E_0 \propto \omega$

If the rotational velocity ($\omega$) of the dynamo armature is increased by four times, then the induced EMF will also increase by four times.

Let the initial rotational velocity be $\omega_1$ and the initial induced EMF be $E_1$.

$E_1 = NBA\omega_1$

Let the new rotational velocity be $\omega_2$ and the new induced EMF be $E_2$.

Given $\omega_2 = 4\omega_1$.

Then, the new induced EMF will be:

$E_2 = NBA\omega_2 = NBA(4\omega_1) = 4(NBA\omega_1) = 4E_1$

Thus, the induced EMF of the dynamo will be four times the original value.