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Question
State the average or mean value of an alternating emf? Obtain the expression for it.
Solution
- average or mean value of A.C. is the average of all values of the voltage (or current) over the one-half cycle.
- Since the average value of sin ωt over a cycle is zero, the average value over a full cycle is always zero.
- Hence, the mean value of AC over a cycle has no significance and the mean value of AC is defined as the average over half cycle.
- The average value of sinθ in the range 0c to πc is given as,
(sin θ) = `(int_0^pi sin theta "d"theta)/(int_0^pi "d"theta) = ([-cos theta]_0^pi)/([theta]_0^pi) = 2/pi = 0.637` - Therefore, average value of emf = 0.637 × peak value i.e., eav = 0.637 e0
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