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Q.
An alternating voltage is given by $E =100\,sin (\omega +\frac{\pi}{6})\,V $ The voltage will be
maximum for the first time when is [$T$ = periodic time)
Given, alternating voltage is
$E=100 \sin \left(\omega t+\frac{\pi}{6}\right) V$
The voltage will be maximum, when
$ \sin \left(\omega t+\frac{\pi}{6}\right)=1 $
$\Rightarrow \,\,\,\,\,\sin \left(\omega t+\frac{\pi}{6}\right)=\sin \frac{\pi}{2}$
$\Rightarrow \,\,\,\, \omega t+\frac{\pi}{6}=\frac{\pi}{2} $
$\Rightarrow \,\,\,\,\, \omega t=\frac{\pi}{3} $
$\Rightarrow \,\,\,\,\, t=\frac{\pi}{3 \omega}=\frac{\pi \times T}{3 \times 2 \pi} \,\,\,\,\,\,\left[\because \omega=\frac{2 \pi}{T}\right]$
$=\frac{T}{6} $
Thus, the voltage will be maximum for the first time when $t=\frac{T}{6}$.