5. Circuit analysis. The circuit illustrated below is driven by a generator that supplies an alternating EMF of the form V(t) = Vo cos wt. The current through the resistor can be expressed as I(t) Io cos(wt), where I and depend on the position of the == switch S. L C C 1 S 2 www R (a) For any driving frequency w, find the complex impedance Zo of the circuit when the switch is open. Also find the complex impedance of the circuit when the switch is in position 1 (Z₁) and when it's in position 2 (Z2). 1 (b) Consider the switch in position 1. For a fixed Vo, find the angular frequency ŵ for which the current I has a maximal amplitude. What is the value of the amplitude Io and the average power dissipated P when w = ŵ? = Now suppose that the generator provides a voltage with amplitude 325 V at a frequency f = 50 Hz. When the switch is open, the current I leads the voltage V by a phase o π/4. When the switch is in position 1, the current lags the voltage by = tan¯¹(-1/2). When the switch is in position 2, the peak current is 2.5 A. (c) Find the values of R, L, and C.

Fig: 1