CORRECT ANSWER IS 229.64 PLEASE SHOW ME HOW TO GET THIS ANSWER A 14 Ohm resistor

Question

CORRECT ANSWER IS 229.64

PLEASE SHOW ME HOW TO GET THIS ANSWER

A 14 Ohm resistor, a capacitor, and a inductor are connected in series to an AC voltage source with a maximum voltage of 81 volts to form a RLC circuit. At some frequency the inductive reactance is 2 Ohms less than the capacitive reactance.  What is the average power for this circuit at the frequency in Watts?

A 14 Ohm resistor, a capacitor, and a inductor are connected in series to an AC voltage source with a maximum voltage of 81 volts to form a RLC circuit. At some frequency the inductive reactance is 2 Ohms less than the capacitive reactance.  What is the average power for this circuit at the frequency in Watts?

229.64 ± 10%

Explanation / Answer

Vrms = Vmax/ sqrt(2) = 81/sqrt(2) =57.3 V

Impedance Z= sqrt ( 14^2 + (-2)^2) =14.142 ohms

power = Vrms^2 / Z = 57.3^2 /14.142 =232 power factor = cos (taninverse(-2/14) =0.98995

therefore power = 232*0.98995 =229.67W

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