Physics

Problem

A series RLC circuit consists of a resistor R, an inductor L and a capacitor C connected to an alternating source of angular frequency

\omega

. a. (a) Derive an expression for the magnitude of the impedance

Z

of the circuit in terms of R, L, C and

\omega

. b. (b) Show that the condition

Z = R\sqrt{2}

leads to the equation

\lvert \omega L - 1/(\omega C) \rvert = R

. c. (c) For

R = 20\,\text{Ω}

L = 0.20\,\text{H}

and

C = 50\,\mu\text{F}

, calculate the two angular frequencies that satisfy the condition in part (b). Take

\pi = 3.14