The peak value of a sine wave is 200 V. Its average value is

Question

Examoogle · Accepted Answer

127.4 V

Explanation: Given: Peak value of sine wave (Vm) = 200 V

Formula Used: $$V_{avg} = \frac{2 	imes V_m}{\pi}$$

Steps: Identify the given value: The peak value ($V_m$) of the sinusoidal voltage is given as 200 V.. State the formula for average value: For a pure sinusoidal wave, the average value over a half cycle is defined by the formula $V_{avg} = \frac{2V_m}{\pi}$.. Perform the calculation: Substitute $V_m = 200$ and $\pi \approx 3.14159$ into the formula: $V_{avg} = \frac{2 	imes 200}{3.14159} = \frac{400}{3.14159} \approx 127.32$ V.

Answer: A is correct because the average value of a sinusoidal wave is $2/\pi$ times its peak value, which equals approximately 127.4 V.

Exam Tip: Remember that for a full cycle of a pure sine wave, the average value is 0. The value $127.4$ V is specifically the average over a half-cycle, which is standard in electrical AC circuit analysis.

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