An AC voltage of the form v = 100 sin 1 000t, where v is in volts and t is in se

Question

An AC voltage of the form v = 100 sin 1 000t, where v is in volts and t is in seconds, is applied to a series RLC circuit. Assume the resistance is 345 , the capacitance is 4.80 µF, and the inductance is 0.500 H. Find the average power delivered to the circuit

An AC voltage of the form -100 sin 1 000t, where v is in volts and t is in seconds, is applied to a series RLC circuit. Assume the resistance is 345 , the capacitance is 4.80 F, and the inductance is 0.500 H. Find the average power delivered to the circuit.

Explanation / Answer

here a sreies RLC circuit where

R = 345 ohm L = 0.500 H C = 4.80 uF = 4.80 x 10-6 F

the voltage eqn

V = 100 sin(1000 t)

where Vm = 100 volt w = 1000 rad/s

as we know that the average power

Pavg = Vrms Irms cosQ

then Vrms = Vm / root(2)

Vrms = 100 / root(2) = 70.710 volt

the total impedence

Z = root [ R2 + ( XL - XC )2 ]

here XL = wL

= 1000 x 0.500 = 500 ohm

and XC = 1 / wC

= 1 / (1000 x 4.80 x 10-6) = 208.333 ohm

so the impedence

Z = root [ (345)2 + ( 500 - 208.333 )2 ]

= root [ 204094.444 ]

= 451.768 ohm

so the current

Im = Vm / Z

= 100 / 451.768 = 0.221352 Amp

so Irms = Im / root(2)

= 0.15651 Amp

and   

cosQ = R / Z

= 345 / 451.768 = 0.76366

so the average power

Pavg = 70.710 x 0.15651 x 0.76366

Pavg = 8.4513 W Ans

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