ECE 201 Spring 2010Homework 33 SolutionsProblem 30(a)Yin(jω) =1R+1jωL= 0.05 −j0.25ωZin(jω) =1Yin(jω)=j20ω5 + jω(b)IL=IinZin(jω)jωL= 10 ×10(i + j)j20= 5√2e−jπ/4⇒ iL(t) = 10 cos(5t − π/4) mAProblem 40Let the impedances of R1, C and R2, L combinations be Z1and Z2respec-tively.Z1=1500+ j(400 × 5 × 10−6)−1= 250(1 − j)Z2="1100+1j(400 × 0.125)#−1= 20(1 + 2j)1Let the phasor current through the source be I.I =V270 − j210⇒ VC= I × 250(1 − j)=120√2(1.0256 − j0.1282)⇒ vC(t) = 124.032 cos(400t − 7.125◦) VIL= V270 − j210! R2R2+ jωL!=V × 100(270 − j210)(100 + j50)=240√2(0.00128205 + j0.0002564)⇒ iL(t) = 0.3138 cos(400t + 11.3099◦)
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