Explanation

(d) As the coil rotated, angle $\theta$ (angle which normal to the coil makes with B at any instant $t$) changes, therefore magnetic flux $\phi$ linked with the coil changes and hence an emf is induced in the coil. At this instant$\ t$, if $e$ is the emf induced in the coil, then
$\ \ \ \ \ \ \ e = - \frac{d\phi}{dt} = - \frac{d}{dt}\ \left( NAB\cos{\omega t} \right)$
Where N is number of turns in the coil.
or $e = - NAB\frac{d}{dt}(\cos{\omega t})$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = - NAB( - \sin{\omega t})\omega$
or $\ \ \ \ \ \ e = NAB\omega\sin{\omega t}$
The induced emf will be maximum
When $\sin{\omega t} = maximum = 1$
$\therefore\ \ \ \ \ \ \ e_{\max} = e_{0} = NAB\omega \times 1$
or $\ \ \ \ \ \ \ \ \ \ \ e = e_{0}\sin{\omega t}$
Therefore, $e$ would be maximum, hence current is maximum (as$\ i_{0} = e_{0}/R),\ $when $\theta = 90{^\circ}$, $ie,$ normal to plane of coil is perpendicular to the field or plane of coil is parallel to magnetic field.