Question

The average emf during the positive half cycle of an AC supply of peak value $E_0$ is :

• A. $\frac{E_0}{\pi }$
• B. $\frac{E_0}{\sqrt{2\pi }}$
• C. $\frac{E_0}{2\pi }$
• D. $\frac{2E_0}{\pi }$

Answer 1

Answer: (D)

$\frac{2E_0}{\pi }$

$E=E_{o}Sinwt$

for $E_{avg}=\frac{{\int }_0^{\frac{\pi }{w}}{E}_{o}Sinwtdt}{{\int }_0^{\frac{\pi }{w}}dt}$
$=\frac{E_{o}2/\omega }{\frac{\pi }{w}}$

$=\frac{2}{\pi }{E}_o$