Consider the circuit that is connected to an external source as shown in figure 1. Radio waves from a nearby radio station are the external AC source. As- sume VAC(t) = V0 cos(?t+ ?) where R,L,V0,?,? are arbitrary positive constants.

N R C 0000 Figure 1: RLC circuit for the FM receiver in parallel with an external source.Figure 1: RLC circuit for the FM receiver in parallel with an external source. Use the relationship between voltage and current for each circuit '3 element and the identity I = Q to: (a) Find the current across the resistor as a function of time: I R(t). ( 5 pts) (b) Find the current across the capacitor as a function of time: Io(t). ( 5 pts) (c) Find the current across the inductor as afunction of time: IL(t). (5 pts) (d) Let's denote the total current in the circuit by IT(t) = A cos(Qt+q)+B siI1(Qt+ 915). Find A, B. Hint: the result shows that Ic(t) is delayed with respect to I R(t) one quarter of a cycle, while I L (t) is advanced with respect to I R(t) one quarter of a cycle. This fact motivates the concept of electrical impedance in EE. ( 5 pts}