A resistor, inductor, and capacitor are connected in parallel to an ac source with voltage amplitude V and angular frequency ω. Let the source voltage be given by v=Vcosωt. A) Show that the instantaneous voltages vR, vL, and vC at any instant are each equal to v and that i=iR+iL+iC, where i is the current through the source and iR, iL, and iC are the currents through the resistor, the inductor, and the capacitor, respectively.
B) What is the phase of iR with respect to v?
C) What is the phase of iL with respect to v?
D) What is the phase of iC with respect to v?
E) Draw a phasor diagram for the currents i, iR, iL, iC.
F) Use the phasor diagram of part (e) to find the current amplitude I for the current i through the source. Express your answer in terms of the variables IR, IC and IL .
G) Show that the result of part (f) can be written as I=V/Z, with 1/Z=sqrt(1/R^2+(ωC−1/ωL)^2).