Question

A 130 V (rms), 62 Hz power supply is connected to an RLC series circuit with R = 145 Ω , L = 1.35 mH , and C = 31.0 μF .

Part A: Find the reactance of the capacitor

Part B: Find the reactance of the inductor

Part C: Find the circuit impedance

Part D: Find the peak current

Answer 1

sol: Given data Voltage, V = 130v f = 62Hz R = 145 ohms L = 1. 35mH C = 31. 0 muF part A: Reactance of capacitor is given by the formula Xc = 1/2pifc XC = 1/2pi times 62 times 31. 0 times 10^-6 XC = 1/0. 012 XC = 83. 33 ohms Part B: Reactance of the inductor is given by XL = 2pifL = 2pi times 62 times 1. 35 times 0. 001 = 0. 52 ohms 1MH = 10^-3H Part C: circuit impedance (Z) Z = R + XC + XL = 145 + 83. 33 + 0. 52 = 228. 85 ohm Part D: peak current, Ipeak = Vpeak/R where Vpeak = VRms times squareroot 2 VR = 130 times squareroot 2 Vp = 183. 84 volts Therefore Ipeak = 183. 84/145 Ipeak = 1. 26A.