Question

31.5 power in alternating - current circuits
a series circuit consists of a 15 - ω resistor, a 25 - mh inductor, and a 45 - μf capacitor. if the frequency is 100.0 hz, the power factor is
0.61
1.0
0.27
0.43
0

Explanation:

Step1: Calculate inductive reactance \(X_L\)

The formula for inductive reactance is \(X_L = 2\pi fL\).
Given \(f = 100.0\space Hz\) and \(L=25\times10^{- 3}\space H\),

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Step2: Calculate capacitive reactance \(X_C\)

The formula for capacitive reactance is \(X_C=\frac{1}{2\pi fC}\).
Given \(f = 100.0\space Hz\) and \(C = 45\times10^{-6}\space F\),

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Step3: Calculate impedance \(Z\)

The formula for impedance in an \(RLC\) series circuit is \(Z=\sqrt{R^{2}+(X_L - X_C)^{2}}\).
Given \(R = 15\space\Omega\), \(X_L\approx15.7\space\Omega\), \(X_C\approx35.4\space\Omega\)

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Step4: Calculate power factor \(\cos\varphi\)

The formula for power factor is \(\cos\varphi=\frac{R}{Z}\).

$$ \cos\varphi=\frac{15}{24.8}\approx0.61 $$

Answer:

0.61