Question

Determine the power delivered to an element at t=4 ms if the current through the element is given by
i=7cos60πt A
evaluate your answer when the voltage is related to the current by the relationship v= 5 di/dtv=5di/dt

Answer 1

Determine the power delivered to an element at t = 4 ms if the current through the element is given by i = 7cos60πt. evaluate your answer when the voltage is related to current by the relationship v = 5 di/dt

solution : we know, power delivered by element is given by, P = Vi

= (5 di/dt)(7cos60πt)

= 35 [d(7cos60πt)/dt] (cos60πt)

= 35[ -7 × 60π sin60πt ] (cos60πt)

= -35 × 7 × 60π sin60πt cos60πt

now putting, t = 4ms = 0.004 sec

= -35 × 7 × 60π sin(60π × 0.004) cos(60π × 0.004)

= -46158 sin(0.24π) cos(0.24π)

= -46158 × 0.499

= -23032.842 ≈ -23033 W

= -23.033 kW

Therefore the power delivered by element is 23.033 kW.