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Download Chapter 28 Problem 20 † Given R = 470 Ω C = 10 µF L = 750 mH
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Chapter 28 Problem 20 † Given R = 470 Ω C = 10 µF L = 750 mH Vrms = 6.3 V f = 60 Hz Solution Find the rms current for each of the components if they are connected to the power supply. Resistor With the resistor attached to the power supply the rms current can be found through Ohm’s law. Irms = 6.3 V Vrms = R 470 Ω Irms = 0.0134 A = 13.4 mA Capacitor First find the angular frequency. ω = 2πf = 2π(60 Hz) = 120π rad/s The capacitive reactance is then XC = 1 1 = ωC (120π rad/s)(10 × 10−6 F ) XC = 265 Ω Now with the capacitor attached to the power supply the rms current can be found through Ohm’s law and replacing the resistance with the capacitive reactance. Irms = 6.3 V Vrms = XC 265 Ω Irms = 0.0238 A = 23.8 mA Inductor The inductive reactance is XL = ωL = (120π rad/s)(0.75 H) XL = 283 Ω Now with the inductor attached to the power supply the rms current can be found through Ohm’s law and replacing the resistance with the inductive reactance. Irms = Vrms 6.3 V = XL 283 Ω Irms = 0.0223 A = 22.3 mA † Problem from Essential University Physics, Wolfson
