# Problem: A RLC series circuit with an AC voltage source has a  200 Ω resistor and a 25.0 mH inductor. At 8000 Hz, the phase angle is 45.0°. (a) What is the impedance? (b) Find the circuit’s capacitance. (c) If Vrms = 408 V is applied, what is the average power supplied?

###### FREE Expert Solution

Impedance, resistance, capacitive reactance, and inductive reactance are related by:

$\overline{){\mathbf{Z}}{\mathbf{=}}\sqrt{{\mathbf{R}}^{\mathbf{2}}\mathbf{+}{\mathbf{\left(}\mathbf{X}}^{}}}$L-XC)2, where R is the resistance.

Inductive reactance:

$\overline{){{\mathbf{X}}}_{{\mathbf{L}}}{\mathbf{=}}{\mathbf{2}}{\mathbf{\pi }}{\mathbf{f}}{\mathbf{L}}}$, where f is the frequency and  L is the inductance.

Capacitive reactance:

$\overline{){{\mathbf{X}}}_{{\mathbf{C}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}\mathbf{\pi }\mathbf{f}\mathbf{C}}}$, where C is the capacitance.

Power:

$\overline{){{\mathbf{P}}}_{\mathbf{a}\mathbf{v}\mathbf{g}}{\mathbf{=}}\frac{{{\mathbf{V}}_{\mathbf{r}\mathbf{m}\mathbf{s}}}^{\mathbf{2}}}{\mathbf{Z}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\varphi }}}$ ###### Problem Details

A RLC series circuit with an AC voltage source has a  200 Ω resistor and a 25.0 mH inductor. At 8000 Hz, the phase angle is 45.0°.

(a) What is the impedance?

(b) Find the circuit’s capacitance.

(c) If Vrms = 408 V is applied, what is the average power supplied?