Question

What will happen when the frequency of rotation in an AC dynamo is doubled?

Answer 1

Hint: As the coil rotation frequency rises, so does the magnetic flux linkage because the coil rotation frequency enhances the change in the current direction. The more significant the difference in the current direction, the greater the variation in magnetic flux change.

Complete step by step solution:
Magnetic flux inside the AC dynamo coil is given by:
$\phi = \vec{B} \cdot \vec{A} = BA cos \theta$
where, B is the magnetic field going through a dynamo coil.
A is the area vector normal to the coil plane.
Let w is the angular frequency with which coil is rotating, then angle between B and A will be:
$\theta = wt$
And, $ w = 2 \pi f$
where, f is the frequency of coil’s rotation.
Now, magnetic flux will be:
$\phi = BA cos (2 \pi ft)$
Magnetic flux will get doubled if frequency is doubled.
Now, Induced emf is given by the rate of change of magnetic flux.
$e = - \dfrac{d \phi}{dt}$
$e = - \dfrac{d (BA cos (2 \pi ft))}{dt}$
$e = BA(2 \pi f) sin (2 \pi f t)$
Therefore, induced emf in the coil will also get doubled while doubling the frequency and so, the induced current will also be doubled.

Note: An alternating current generator is a machine that transforms the mechanical energy into electric energy; when the coil turns between the two poles of the electromagnet, it catches the magnetic flux lines, which produce the induced emf and produced electric current that can be transported through wires for long distances.