A LCR series circuit driven with $E_{rms} = 90 ext{ }V$ at frequency $f_{d} = 30 ext{ }Hz$ has res

Question

A LCR series circuit driven with $E_{rms} = 90\text{ }V$ at frequency $f_{d} = 30\text{ }Hz$ has resistance $R = 80\Omega$, an inductance with inductive reactance $X_{L} = 20.0\Omega$ and capacitance with capacitive reactance $X_{C} = 80.0\Omega$. The power factor of the circuit is

$\_\_\_\_$ .

Accepted Answer

Sol. [Key Concept: Power factor $cos\varphi = \frac{R}{Z}$ with $Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}} = \sqrt{80^{2}{+ 60}^{2}} = 100\ \Omega$.]Power factor is $cos\phi = \frac{R}{Z}$$$\begin{matrix} & Z = \sqrt{R^{2} + \left( X_{L} - X_{C} ight)^{2}} = 100\Omega \ & cos\phi = \frac{80}{100} = 0.8 \end{matrix}$$

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