A resistor, inductor, and capacitor are connected in parallel to an ac source with voltage amplitude V and angular frequency ?. Let the source voltage be given by ? = V cos ?t.

(a) Show that the instantaneous voltages ?_R, ?_L, and ?_C at any instant are each equal to ? and that i = iR + i_L + i_C, where I is the current through the source and i_R, i_L, and I_C, are the currents through the resistor, the inductor, and the capacitor, respectively.

(b)What are the phases to represent i, i_R, i_L and i_C with respect to ?? Use current phasor to represents I, i_R, i_L, and i_C in a phasor diagram, show the phases of the four currents with respect to ?.

(c)Use the phasor diagram of part (b) to show that the current amplitude I for the current I through the source is given by

(d) Show that the result of part (c) can be written as

1 = VIR + (Ic - IL). %3D V/Z, with 1/Z = V1/R + (@C 1/@L)? %3D %3D