Question

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

Answer 1

Hint:: The number of cycles per second made by voltage induced in the armature is the frequency of the generator that is if the armature rotates at speed of $60$ revolutions per second then the generated voltage will be $60$ cycles per second.

Formula used:
We will use the general formula of emf induced in the coil, it is
${\displaystyle \frac{-d\varphi }{dt}}=BA\omega \sin \omega t$
where $A$ is the area of the coil, $N$ is the number of turns, $t$ is time and $\omega$ is the angular velocity and another formula used is $\varphi =BA\cos \omega t$ .

Complete step by step answer:
We know that if $A$ is the area of the coil, $N$ is the number of turns, $\omega$ being the angular velocity of the armature, then the flux through each turn in time $t$ is given by the formula $\varphi =BA\cos \omega t$.
Now we know that by Faraday's law the emf induced in each turn of the coil is,
${\displaystyle \frac{-d\varphi }{dt}}=BA\omega \sin \omega t$
Then we see that the total induced emf in the coil will become,
$\epsilon =NBA\omega \sin \omega t$
Now we see that $\epsilon$ is directly proportional to $\omega$, so when we double the rotational velocity that is multiplying it by $2$, we will get our equation as $\epsilon =2NBA\omega \sin \omega t$ that is the emf induced will also get doubled.

Therefore when we double the velocity of a dynamo armature then the induced emf will also get doubled.

Note:AC dynamo is the device which is used to convert mechanical energy into electrical energy. It consists of a rectangular coil rotating in a uniform magnetic field. The emf induced will always be directly proportional to all the terms in the equation therefore doubling any other terms of the equation will double the emf induced. We will notice that the frequency of the alternating current will also get doubled.