Use the worked example above to help you solve this problem. A series RLC AC cir

Question

Use the worked example above to help you solve this problem. A series RLC AC circuit has resistance R = 2.90 x 10^2 ohm, inductance L = 0.500 H, capacitance C = 3.50 mu F, frequency f = 60.0 Hz, and maximum voltage max delta V max= 3.00 x 10^2 V. (a) Find the impedance. (b) Find the maximum current In the circuit. (c) Find the phase angle. (d) Find the maximum voltages across the elements. Analyze a series RLC AC circuit for which R = 330 ohm, L = 0.300 H, C = 22.5 mu F, f = 50.0 Hz, and max = 325 V. (a) Find the impedance. (b) Find the maximum current. (c) Find the phase angle. (d) Find the maximum voltages across the elements.

Explanation / Answer

a) Impdance = R + j ( XL - XC)

R = 290 ohm

XL = 2pifL = 2 pi x 60 x 0.5 = 188.50 ohm

Xc = 1 / 2pifC = 1 / (2pi x 60 x 3.50 x 10^-6) = 757.89 ohm

impedance = 290 + j (188.50 - 757.89) = 290 - j569.38

magnitude Z = sqrt(290^2 + (-569.38)^2) = 638.98 ohm

b) Imax = Vmax / Z = 300 / 625.94 = 0.47 A

c) phase angle = tan^-1 [ (XL - Xc) / R ] = tan^-1 ( -569.38 / 290) = -63 deg

d) VR = I R = 0.47 x 290 = 136.3 volt

VL =I XL   = 0.47 x 188.50 = 88.60 volt

Vc = I Xc =0.47 x 757.89 =356.21 volt

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similarly you can do 2nd part.

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