Question

An AC voltage is given by. $E=E_0\sin \frac{2\pi t}{T}$. Then the mean value of voltage calculated over any time interval of $T/2$ seconds.

• A. Is always zero
• B. Is never zero
• C. Is $\left(2e_0/\pi \right)$ always
• D. May be zero

Answer 1

The correct option is A Is always zero

$E=E_{0}sin\frac{2\pi t}{T}$

Mean voltage calculated over time interval $\frac{T}{2}$ is,

$=\frac{{\int }_0^{\frac{T}{2}}Edt}{{\int }_0^{\frac{T}{2}}dt}$

$=\frac{2}{T}{\int }_0^{T}sin\left(\frac{2\pi }{T}t\right)dt$

$=\frac{1}{\pi }{\int }_0^{T}sin\left(\frac{2\pi }{T}t\right)d\left(\frac{2\pi }{T}\right)$

$=\frac{1}{\pi }{[-\cos \frac{2\pi }{T}t]}_0^T$

$=\frac{1}{\pi }[-1+1]$

$=0$