Question

An alternating voltage is represented as E = 20 sin 300 t. The average value of voltage over one cycle will be
(a) Zero
(b) 10 volt
(c) 20 √2 volt
(d) $\frac{20}{\sqrt{2}} volt$

Answer 1

Answer : option (a)

explanation : An alternating voltage is represented as $E=200sin300t$.

we have to find average value of the voltage over one cycle .

we know, $E_{av}=E_0\int\limits^{2\pi}_0{sin\omega t}\,dt$

$E_{av}=20\int\limits^{2\pi}_0{sin300t}\,dt$

$=20\left[\frac{cos300t}{300}\right]^{2\pi}_0$

$=\frac{20}{300}[cos600\pi-cos0]$

= 0

hence, average value of voltage over one cycle will be zero.