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Electrostatic Potential And Capacitance

Question

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Give expression for average value of a.c. voltage V = V₀ sin ωt over time interval t = 0 to $t = \frac{π}{ω} .$

Solution

A.C. voltage, V= V₀ sin ωt

As,
$t = \frac{π}{ω} = \frac{1}{2} . \frac{2 π}{ω} = \frac{1}{2} T,$

therefore, first half cycle (T/2).

Hence, average value of AC voltage, $E_{av} = \frac{2 V_{0}}{π}$

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