A resistor and an inductor are connected in parallel across an emf = Emax as shown

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A resistor and an inductor are connected in parallel across an emf ← = Emax as shown in Figure. Show that

(a) The current in the resistor is IR = (←max /R) cos ωt,

(b) The current in the inductor is IL = (←max /XL) cos (ωt – 90°), and

(c) I = IR + IL = Imax cos (ωt – δ), where tan δ = R/XL and Imax = ←max/Z with Z-2 = R + XL-2.

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