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31.56: 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 w. Let the source voltage be given by v V cos wt. a) Show that the instantaneous voltages vR, VIL, and ve at any instant are equal to i-k-il+ic. where i is the current through the sou the resistor, inductor, and the capacitor. b) What are the phases of IR, iL, and ic with respect to v? Use current phasors to represent i, in,le and ic. c) Use the phasor diagram of part b) to show that the current amplitude i for the current I through the source is given byl ((Ic-1)205 d) Show that the result of part c) can be written as I-V/Z with 1/22-1/R2+(uC-1/uL)2 v and that rce and iR.L and ic are currents through In a phasor diagram, show the phases of these four currents with respect to v. Show all steps

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