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?
  1. $\frac{\mathrm{T}}{6}$
  2. $\frac{\mathrm{T}}{3}$
  3. $\frac{T}{2}$
  4. $\frac{\mathrm{T}}{12}$

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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