Question

An AC voltage is given by $E=E_o\sin \frac{2\pi t}{T}$.Then the mean voltage calculated over the interval of $\frac{T}{2}$ second.

• A. is always zero
• B. is never zero
• C. is always $\frac{2E_o}{\pi }$
• D. maybe zero

Answer 1

The correct option is C is always $\frac{2E_o}{\pi }$

$E=E_o\sin \frac{2\pi t}{T}Meanvalue=\frac{1}{1/2}{\int }_0^{T/2}{E}_0\sin \frac{2\pi t}{T}dt\frac{2}{T}{E}_0\times \frac{-T}{2\pi }\left[\cos \frac{2\pi t}{T}\right]-\frac{E_0}{\pi }[\cos \pi -\cos 0]-\frac{E_0}{\pi }[-1-1]-\frac{E_0}{\pi }-2=2\frac{E_0}{\pi }$