Write the equation for the maximum $emf$ in an $AC$ generator.

(N/A) In an $AC$ generator,the magnetic flux $\phi$ linked with the coil rotating with angular velocity $\omega$ in a magnetic field $B$ is given by $\phi = NBA \cos(\omega t)$,where $N$ is the number of turns and $A$ is the area of the coil.
According to Faraday's law of induction,the induced $emf$ is $\epsilon = -\frac{d\phi}{dt}$.
Substituting $\phi$,we get $\epsilon = -\frac{d}{dt}(NBA \cos(\omega t)) = NBA\omega \sin(\omega t)$.
The maximum value of $emf$ $(\epsilon_{max})$ occurs when $\sin(\omega t) = 1$.
Therefore,the equation for maximum $emf$ is $\epsilon_{max} = NBA\omega$.