10) An AC source with deltaV=150 sin (3000t) is applied to a series RLC circuit
ID: 1391909 • Letter: 1
Question
10) An AC source with deltaV=150 sin (3000t) is applied to a series RLC circuit , with R=200 omega, L=0.1 H, and C=3.3 microF. What are the impedance Z and the phase angle theta? What is the maximum current delivered by the source? What is the average power dissipation in an RLC series circuit? 10) An AC source with deltaV=150 sin (3000t) is applied to a series RLC circuit , with R=200 omega, L=0.1 H, and C=3.3 microF. What are the impedance Z and the phase angle theta? What is the maximum current delivered by the source? What is the average power dissipation in an RLC series circuit?Explanation / Answer
Xe = R = 200 Ohm angle 0
XL = wL = 3000 x 0.1 = 300 Ohm angle 90 degree
Xc = 1/wC = 1 / (3000 x 3.3 x 10^-6) = 101.01 Ohm Angle -90 degree
Z = R + j(XL - Xc )
= 200 + j ( 300 - 101.01) = 200 + j199
|Z| = sqrt(200^2 + 199^2) = 282.13 ohm
Phase angle phi= tan^-1 (199/200) = 44.86 degrees
Imax = Vmax / Z = 150 / 282.13 = 0.532 A
Average Power = ZI^2 cosphi /2
= 282.13 x 0.532^2 x cos44.86 / 2 = 28.26 W
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