# In an AC generator, a coil with N turns, all of the same area A and total resistance R , rotates with frequency $\dpi{100} \omega$ in a magnetic field B . The maximum value of emf generated in the coil is Option 1) $NAB\omega$ Option 2) $NABR\omega$ Option 3) $NAB$ Option 4) $NABR$

As we learnt in

Motional E.m.f due to rotational motion -

Semicircle conducting loop

$\varepsilon = \frac{1}{2}Bwr^{2}$

$i = \frac{Bwr^{2}}{2R}$

- wherein

Flux at any instant is$\phi=BA\ cos\omega t$

$emf=(BA\;\omega sin \omega t)N$

maximum $emf=NBA \omega$

Option 1)

$NAB\omega$

This option is correct

Option 2)

$NABR\omega$

This option is incorrect

Option 3)

$NAB$

This option is incorrect

Option 4)

$NABR$

This option is incorrect

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