Reference no: EM13998253
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 = Vcos ωt.
(a) Show that the instantaneous voltages vR, vL, and vC at any instant arc 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 are the phases of iR, iL, and iC with respect to v? Use current phasors to represent i, iR, iL, and iC. In a phasor diagram, show the phases of these four currents with respect to v.
(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 I = √(IR2 + (IC - IL))2.
(d) Show that the result of part (c) can be written as I = V/Z with 1/Z = √(1/R2 + (ωC -1/ωL))2.
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