In the circuit shown, the AC voltage source supplies an rms voltage of 115 V and
ID: 1444938 • Letter: I
Question
In the circuit shown, the AC voltage source supplies an rms voltage of 115 V and the circuit has R_1 = 3.15 k Ohm and C = 1 mu F. At what frequency should the voltage source oscillate so that the voltage current will leand the voltage by 23.8 degree? f= Did you remember to convert from omega to f? At this frequency, what is the rms potential drop across the resistor? V_rms R = At this frequency, what is the rms potential drop across the capacitor? V_rmsC = At this frequency, what is the rms potential drop across both the resistor and the capacitor combined? V_rmsTotal = (V_rmsR^2 + V_rmsC^2)^0.5. As a check, what should this equal? What is the average power consumed by the circuit? P_avg =Explanation / Answer
1) phase angle = - 23.8 deg
tan23.8 = -(XL - Xc) / R
and xL = 2 pi f L = 0 and Xc = 1 (2 pi f C)
3150 x tan23.8 = 1 / (2 x pi x f x 1x 10^-6)
f = 114.6 Hz
2) Xc = 3150tan23.8 = 1389.32 ohm
|Z| = sqrt(R^2 + Xc^2) = sqrt(3150^2 + 1389.32^2) = 3442.77 ohm
Irms = Vrms / |Z| = 0.0334 A
Vr = I R = 0.0334 x 3150 = 105.22 volt
3) Vc = 1389.32 x 0.0334 = 46.41 volt
4) V = sqrt(Vr^2 + Vc^2 ) = 115 volt
5) P = Vrms^2 / Z = 115^2 / 3442.77 = 3.84 W