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Question

In an AC generator, a coil with N turns, all of them has same area A and total resistance R, rotates with an angular frequency ω in a magnetic field B. The peak value of current in the coil is-

A
NBAωR
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B
NBAR
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C
NBAωsinωtR
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D
NBAωcosωtR
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Solution

The correct option is A NBAωR
For a loop having N turns, the total induced emf across the two ends of the loop is,

|E|=Ndϕdt=Nddt(BAcosθ)

|E|=Nddt(BAcosωt) [θ=ωt]

|E|=NBAωsinωt=E0sinωt

Where, E0 is the peak emf.

Hence, the peak current of the loop is,

i0=E0R=NBAωR

Hence, (A) is the correct answer.
AC generator works on the principle of Faraday's law of electromagnetic induction, which states that if the flux associated with a conducting coil changes, an induced emf is produced in the coil, and if the coil is closed, a current flows through the coil.

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