CBSE Class 12 Physics 2023: question 28

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Step-by-step solution

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1. Principle: An ac generator works on electromagnetic induction. Whenever the magnetic flux linked with a coil changes, an emf is induced in it.

   1 mark

2. Working: A coil (armature) of $N$ turns and area $A$ is rotated mechanically with constant angular speed $\omega$ in a uniform magnetic field $\vec{B}$. As the coil rotates, the angle between its area vector and $\vec{B}$ changes continuously, so the flux through it changes and an emf is induced. The emf is taken out through slip rings and carbon brushes to the external circuit.

   1 mark

3. Expression: At time $t$ the angle is $\theta =\omega t$, so the flux through each turn is ${\varphi }_B=BA\cos \omega t$. By Faraday's law, $\epsilon =-N\frac{d{\varphi }_B}{dt}=-NBA\frac{d}{dt}(\cos \omega t)$.

   ½ mark

4. Therefore $\epsilon =NBA\omega \sin \omega t={\epsilon }_0\sin \omega t$, where ${\epsilon }_0=NBA\omega$ is the peak emf.

   ½ mark

Answer: ε = NBAω sin ωt

Revise the chapter

• Chapter: Electromagnetic Induction (notes, formulas, where marks are lost and every past question)