1. A series RLC circuit has R = 210 ohms, L = 0.382 H, and C = 0.15 micro F. The

Question

1. A series RLC circuit has R = 210 ohms, L = 0.382 H, and C = 0.15 micro F. The circuit is connected to a source with Vrms =42.0 V. Determine the impedance of the circuit at f = 1800 Hz. Determine the total current from the source. Determine the capacitor Vrms, the inductor Vrms, the resistor Vrms, and the power delivered by the source.

2. For the circuit elements given in question 1, determine the resonant frequency, fo, and construct a phasor diagram roughly to scale at the frequency given above. Does the voltage for the circuit lead or lag the current at 1800 Hz?

Explanation / Answer

1) Z = sqrt(R^2 + ( w L - 1/w C)^2)

= sqrt( 210^2 + (2*pi*1800*0.382 - 1/(2*pi*1800*0.15E-6))^2)= 3737 ohms

Irms = V/Z = 42/3737=0.0112 A

I max = 0.0112*sqrt(2)= 0.0158 A

Vcapacitor = Xc Irms = 0.0112/(2*pi*1800*0.15E-6) = 6.6 V

V inductor = Xl IRMS = 0.0112*2*pi*1800*0.382= 48.4 V

V resistor = R Irms = 210*0.0112= 2.35 V

tan phi = ( Xl - Xc)/R = (2*pi*1800*0.382 - 1/(2*pi*1800*0.15E-6))/210= 17.77

phi = arctan(17.77)= 86.78 degrees

Psource = Irms Vrms cos phi = 0.0112*42*cos(86.78 degrees)= 0.0264 W

2)

f0 = 1/(2 pi ) sqrt(1/LC) = 1/(2*pi)*sqrt(1/(0.382*0.15E-6))=665 Hz

so 1800 is above 665 Hz

so inductor dominates

so voltage leads

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