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The alternating voltage is given by $\mathrm{v}=\mathrm{v}_0 \sin \left(\omega…
The alternating voltage is given by $\mathrm{v}=\mathrm{v}_0 \sin \left(\omega \mathrm{t}+\frac{\pi}{3}\right)$ when will be the voltage maximum for first time?
$\frac{\mathrm{T}}{6}$ $\frac{\mathrm{T}}{3}$ $\frac{T}{2}$ $\frac{\mathrm{T}}{12}$
Solution
$\sin \left(\omega t+\frac{\pi}{3}\right)=1 \quad$ [For voltage to be maximum]
$V=V_0 \sin \left(\omega t+\frac{\pi}{3}\right)$
$\begin{array}{ll}
\therefore \quad & \sin \left(\omega t+\frac{\pi}{3}\right)=\sin \left(\frac{\pi}{2}\right) \\
& \omega t+\frac{\pi}{3}=\frac{\pi}{2} \\
\therefore \quad & \omega t=\frac{\pi}{6} \\
& t=\frac{\pi}{6 \omega} \\
\therefore \quad & =\frac{\pi \times T}{6 \times 2 \pi} \\
& t=\frac{T}{12}
\end{array}$
$\ldots\left(\because \omega=\frac{2 \pi}{\mathrm{~T}}\right)$
Asked in: MHT CET 2024 (16 May Shift 1)
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