Question

The average e.m.f during the positive half cycle of an a.c. supply of peak value $E_0$ is:

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

Answer 1

The correct option is D $\frac{2E_0}{\pi }$

$E=E_{o}sinwt$ it is defined for half cycle

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

$=\frac{{\int }_0^{\frac{\pi }{w}}{E}_{o}sinwtdt}{{\int }_0^{\frac{\pi }{w}}dt}=\frac{2E_o}{\pi }$