5. In the AC circuit depicted in the figure below, the capacitance of the capacitor is C = 0.1 F and the resistance of the resistor, R = 102. The AC generator delivers a voltage &(t) = 20 cos(8t) (V), where t is expressed in seconds, and the natural frequency of the circuit is 1Hz.

(a) Calculate the value of the inductance I and the frequency of the AC generator.

(b) Calculate the complex reactance of all components.

(c) Calculate the complex impedance of the circuit.

(d) Demonstrate that the RMS voltage delivered by the AC generator is

20 / √2(V).

(e) Derive an expression for the power dissipated on the resistor as a function of time.