If the A.C. main supply is given to be 220 V in a circuit. The average emf during a positive half cycle is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 198 V
Given: AC supply, $V_{\text{rms}} = 220\,\text{V}$
For a sinusoidal AC voltage: $v(t) = V_m \sin \omega t$, where $V_m$ is the peak voltage
Relationship: $V_{\text{rms}} = \frac{V_m}{\sqrt{2}} \Rightarrow V_m = V_{\text{rms}} \sqrt{2} = 220 \sqrt{2} \approx 311\,\text{V}$
Average emf during positive half cycle: $V_{\text{avg}} = \frac{1}{\pi} \int_0^\pi V_m \sin \theta \, d\theta = \frac{2 V_m}{\pi}$
$V_{\text{avg}} = \frac{2 \cdot 311}{\pi} \approx 198\,\text{V}$
Answer: $V_{\text{avg}} \approx 198\,\text{V}$