A LCR series circuit driven with V_{rms} = 90 | vedclass

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(A) The power factor of an $LCR$ series circuit is given by $\cos \phi = \frac{R}{Z}$.First, calculate the impedance $Z$ of the circuit using the form

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$0.8$

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(A) The power factor of an $LCR$ series circuit is given by $\cos \phi = \frac{R}{Z}$.First, calculate the impedance $Z$ of the circuit using the formula $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Given values are $R = 80 	ext{ }\Omega$, $X_L = 20.0 	ext{ }\Omega$, and $X_C = 80.0 	ext{ }\Omega$.Substitute the values into the impedance formula:$Z = \sqrt{80^2 + (20 - 80)^2} = \sqrt{80^2 + (-60)^2} = \sqrt{6400 + 3600} = \sqrt{10000} = 100 	ext{ }\Omega$.Now, calculate the power factor:$\cos \phi = \frac{R}{Z} = \frac{80}{100} = 0.8$.

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