Question
Consider a series RLC circuit with R = 15 ohm, L = 184 mH, C = 75 mu F, and a maximum voltage of 149 V. What is the impedance of the circuit at resonance? Z = ohm What is the resonance frequency of the circuit? f = Hz When will the current be greatest: at resonance, at ten percent below the resonant frequency, or at ten percent above the resonant frequency? The current is a maximum at ten percent above the resonant frequency. The current is a maximum at ten percent below the resonant frequency. The current is a maximum at resonance. What is the rms current in the circuit at a frequency of 60 Hz? Irms = A
Explanation / Answer
a. Impedance Z = {R2 + (XL - XC)2} atresonance XL = XC => Z = R Hence impedance atresonance Z = 15 b. Resonancefrequency f = 1/ 2(L * C) = 1/ 2 * 3.14 * ( 184 * 10-3 * 75 *10-6) = 42.86 Hz c. Current I = V/ Z Clearlycurrent is maximum when Z is minimum, i.e. at resonance. => Z = R Hence impedance atresonance Z = 15 b. Resonancefrequency f = 1/ 2(L * C) = 1/ 2 * 3.14 * ( 184 * 10-3 * 75 *10-6) = 42.86 Hz c. Current I = V/ Z Clearlycurrent is maximum when Z is minimum, i.e. at resonance. d. At 60Hz XL = 2* f * L = 2* 3.14 * 60 * 184 * 10-3 = 69.33 XC = 1/ 2 * 60 * 75 * 10-6 = 35.39 Z60 = {152 + (69.33 - 35.39)2} = 37.11 I60 = V/ Z60 = 149/ 37.11 = 4.015 A Irms = I60/ 2 = 4.015/ 2 = 2.439 A = 149/ 37.11 = 4.015 A Irms = I60/ 2 = 4.015/ 2 = 2.439 A