A LCR series circuit driven with $$E_{rms} = 90$$ V at frequency $$f_d = 30$$ 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 _______.

The power factor of an alternating current circuit is defined as the cosine of the phase angle ($$ \phi $$) between the voltage and the current. It can be calculated using the ratio of the real resistance ($$ R $$) to the total impedance ($$ Z $$) of the circuit:

$$ \text{Power Factor} = \cos \phi = \frac{R}{Z} $$

$$ Z = \sqrt{R^2 + (X_C - X_L)^2} $$

$$ Z = \sqrt{80^2 + (80.0 - 20.0)^2} $$

$$ Z = \sqrt{80^2 + 60^2} $$

$$ Z = \sqrt{10000} $$

$$ Z = 100 \ \Omega $$

$$ \cos \phi = \frac{80}{100} $$

$$ \cos \phi = 0.8 $$

Note that the given voltage ($$ E_{rms} $$) and frequency ($$ f_d $$) are not required to find the power factor since the reactances are already provided directly.

The power factor of the circuit is $$ 0.8 $$.