An L-R-C series circuit is connected to an ac source of constant voltage amplitude V and...

An L-R-C series circuit is connected to an ac source of constant voltage amplitude V and variable angular frequency ω. Using the results of Problem 31.49, find an expression for (a) the amplitude V_L of the voltage across the inductor as a function of ω and (b) the amplitude V_C of the voltage across the capacitor as a function of v. (c) Graph V_L and V_C as functions of v for V = 100 V, R = 200 Ω, L = 2.0 H, and C = 0.50 μF. (d) Discuss the behavior of V_L and V_C in the limits v = 0 and For what value of v is V_L = V_C? What is the significance of this value of ω?

31.49 ... An L-R-C series circuit is connected to an ac source of constant voltage amplitude V and variable angular frequency ω. (a) Show that the current amplitude, as a function of ω, is

(b) Show that the average power dissipated in the resistor is

(c) Show that I and P are both maximum when the resonance frequency of the circuit. (d) Graph P as a function of ω for V = 100 V, R = 200 Ω, L = 2.0 H, and C = 0.50 μF. Compare to the light purple curve in Fig. 31.19. Discuss the behavior of I and P in the limits ω = 0 and