Question

an air conditioner connected to a 120 v rms ac line is equivalent to a 16.7 ω resistance and a 1.33 ω inductive reactance in series. calculate (a) the impedance of the air conditioner and (b) the average rate at which energy is supplied to the appliance. (a) number units (b) number units

Explanation:

Step1: Calculate impedance

The formula for impedance \(Z\) in an \(RL\) series circuit is \(Z=\sqrt{R^{2}+X_{L}^{2}}\). Given \(R = 16.7\space\Omega\) and \(X_{L}=1.33\space\Omega\), we substitute these values into the formula:

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Step2: Calculate average power

The formula for average power \(P_{avg}\) in an AC circuit is \(P_{avg}=I_{rms}^{2}R\). First, we find \(I_{rms}\) using \(I_{rms}=\frac{V_{rms}}{Z}\). Given \(V_{rms} = 120\space V\) and \(Z\approx16.75\space\Omega\), then \(I_{rms}=\frac{120}{16.75}\approx7.16\space A\).
Now, using \(P_{avg}=I_{rms}^{2}R\) with \(R = 16.7\space\Omega\) and \(I_{rms}\approx7.16\space A\):

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Answer:

(a) \(16.75\space\Omega\)
(b) \(856.14\space W\)