A 400-Ω resistor and a 6.00-µF capacitor are connected in parallel to an ac generator that...

A 400-Ω resistor and a 6.00-µF capacitor are connected in parallel to an ac generator that supplies an rms voltage of 220 V at an angular frequency of 360 rad/s. Use the results of Problem. Note that since there is no inductor in the circuit, the l/ωL term is not present in the expression for Z. Find (a) the current amplitude in the resistor; (b) the current amplitude in the capacitor; (c) the phase angle of the source current with respect to the source voltage; (d) the amplitude of the current through the generator. (e) Does the source current lag or lead the source voltage?

Problem:

The L−R−C Parallel Circuit. 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 υ = V cosωt. (a) Show that the instantaneous voltages υR,υL and υc at any instant are each equal to υ 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 are the phases of iR ,iL and ic with respect to υ? Use current phasors to represent i, iR ,iL and ic.In a Phasor diagram, show the phases of these four currents with respect to υ. (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 I = V/Z, with