A large air conditioner has a resistance of 9.0 and an inductive reactance of 14

Question

A large air conditioner has a resistance of 9.0 and an inductive reactance of 14 . The air conditioner is powered by a 65.0 Hz generator with an rms voltage of 250 V .

Part A

Find the impedance of the air conditioner.

Express your answer using two significant figures.

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Part B

Find the rms current.

Express your answer using two significant figures.

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Part C

Find the average power consumed by the air conditioner.

Express your answer using two significant figures.

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Explanation / Answer

here,

Inductive reactance, Xl = 14 ohms

resistance, r = 9 ohms

Frequency, f = 65 Hz

Rms volatge, Vrms = 250 V

Part A:
Impedance, Z = sqrt(R^2 + Xl^2)
Z = sqrt(9^2 + 14^2)
Z = 16.643 Ohms

Part b:
Irms = Vrms / Z
Irms = 250/16.643
Irms = 15.021 A

Part C:
Average Power, P = Irms^2 * R
P = (15.021)^2 * 9
P = 2030.674 Watts

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