The L-R-C Parallel Circuit. A resistor, an inductor, and a 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 = Vcos ωt. (a) Show that each of the instantaneous voltages υR, υL, and υC at any instant is equal to u 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, inductor, and 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
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