Question 436: AC fundamentals

Question

An alternating voltage is given by $E=100 \sin \left(\omega+\frac{\pi}{6}\right) \mathrm{V}$. The voltage will be maximum for the first time when is [ $T=$ periodic time)

Accepted Answer

Given, alternating voltage is
$$E=100 \sin \left(\omega t+\frac{\pi}{6}ight) V$$
The voltage will be maximum, when
$$\begin{aligned}
& \sin \left(\omega t+\frac{\pi}{6}ight)=1 \
& \Rightarrow \quad \sin \left(\omega t+\frac{\pi}{6}ight)=\sin \frac{\pi}{2} \
& \Rightarrow \omega t+\frac{\pi}{6}=\frac{\pi}{2} \
& \Rightarrow \quad \omega t=\frac{\pi}{3} \
& \Rightarrow \quad t=\frac{\pi}{3 \omega}=\frac{\pi 	imes T}{3 	imes 2 \pi} \quad\left[\because \omega=\frac{2 \pi}{T}ight] \
& =\frac{T}{6}
\end{aligned}$$
Thus, the voltage will be maximum for the first time when $t=\frac{T}{6}$.

Answer

$\frac{T}{12}$

Answer

$\frac{T}{2}$

Answer

$\frac{T}{6}$

Answer

$\frac{T}{3}$

AC fundamentals

An alternating voltage is given by E=100 \sin \left(\omega+\frac{\pi}{6}\right) \mathrm{V}. The voltage will be maximum for the first time when is [ T= periodic time)

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