Exercise 31.22 Part A Use Eq. cos = R / Z to show that the average power deliver

Question

Exercise 31.22

Part A

Use Eq. cos=R/Z to show that the average power delivered by the source in an LRC series circuit is given by Pav = I2rmsR .

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Part B

An LRC series circuit has 90.0 , and the amplitude of the voltage across the resistor is 34.0 V . What is the average power delivered by the source?

Express your answer with the appropriate units.

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Explanation / Answer

(A) Average Power = Irms^2 Z cos(phi)

= Irms^2 Z (R/Z)

= Irns^2 R

(B) Vrms = 34 / sqrt(2) = 24.04 Volt

R = 90 ohm

Irms = 24.04 / 90 = 0.267 A

Pavg = 0.267^2 x 90 = 6.42 Watt

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