Question

# In an AC generator, a coil with N turns, all of the same area A and total resistance R, rotates with frequency in a magnetic field B. The maximum value of emf generated in the coil is:

A
N.A.B
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B
N.A.B.R
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C
110N.A.B
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D
110N.A.B.R
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Solution

## The correct option is A N.A.BLet at time t=0, the coil is vertical and at time t , plane of coil makes an angle θ with the vertical, then θ=ωt, (ω= uniform angular velocity),in this position, magnetic flux linked with coil will be, ϕ=NBAcosθ, (where, A= area of coil,)or ϕ=NBAcosωt,now, differentiating this equation w.r.t. time, we get dϕdt=ddt(NBAcosωt),or dϕdt=−NBAωsinωt,if e is the emf induced in coil then by Faraday's law, e=−dϕdt=NBAωsinωt,now if, sinωt=1 (maximum),then emax=NBAω,if ω=1rad/s,then emax=NBA

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