In the series ac circuit where R = 420, L = 0.20 H, C =1.2 F (10 -6 ), the ac po
ID: 1672839 • Letter: I
Question
In the series ac circuit where R = 420, L = 0.20 H, C =1.2 F (10-6), the ac power supply is = 60 sin(1500 rad/s t) V. a.) find the impedance Z b.) find the phase angle and explain which is leading inphase, the voltage or the current c.) the rms current in the circuit In the series ac circuit where R = 420, L = 0.20 H, C =1.2 F (10-6), the ac power supply is = 60 sin(1500 rad/s t) V. a.) find the impedance Z b.) find the phase angle and explain which is leading inphase, the voltage or the current c.) the rms current in the circuitExplanation / Answer
Given resistance R = 420 inductance L = 0.20 H Capacitance C = 1.2 F The ac power supply is = 60 sin (1500 rad/s t ) V .........(!) Ac voltage source V = V o sin t (2) comparing equations (1) and (2) is maximum voltage V o = 60 V angular frequency = 1500 rad / s2 frequency of circuit f = / 2 = 1500 / 2*3.14 = 238.85 Hz impedance Z = R2 + (XL - X C ) 2 inductive reactance XL = 2 f L = 2*3.14 * 238.85 * 0.2 = 299.9956 capacitive reactance XC = 1 / 2 f C =1 / ( 2*3.14* 238.85 * 1.2*10-6 ) = 555 There fore impedance Z = (R2 + ( XL - XC ) 2 )1/2 = ( 4202 + ( 299.99 - 555 ) 2 )1/2 = 491.355 phaseangle tan = XL - XC / R = 299.9956 - 555 / 420 = - 31.36 o r m s voltage in the circuit is V r m s = Vo / 2 = 60 / 1.414 = 42.4328 r m s current in thecircuit I r m s = V r ms / Z = 42.43 / 491.355 = 0.086 A