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

JEE Main · 2006 · 30 Apr 2006 · Offline · Electromagnetic Induction

In an AC generator, a coil with N turns, all of the same area A and total resistance R, rotates with frequency

ω

in a magnetic field B. The maximum value of emf generated in the coil is

(A)N.A.B. $ω$ ✓ Correct
(B)N.A.B.R. $ω$
(C)N.A.B
(D)N.A.B.R

Answer: (A)

Solution

A coil of

N

turns, each of area

A

, rotating at angular frequency

ω

in a field

B

links a flux

N B A cos ω t

. The induced emf is minus the time derivative of this, namely

N B A ω sin ω t

, whose peak value is

N A B ω

. The resistance

R

only fixes the current that flows, not the peak emf, so the maximum emf generated is

N A B ω

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option

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