A series RLC circuit driven by a source with an amplitude of 120.0 V and a frequ

Question

A series RLC circuit driven by a source with an amplitude of 120.0 V and a frequency of 50.0 Hz has an inductance of 772 mH, a resistance of 289 ohm, and a capacitance of 46.4 mu F. What are the maximum current and the phase angle between the current and the source emf in this circuit? Your response differs from the correct answer by more than 10%. Double check your calculations. A What are the maximum potential difference across the inductor and the phase angle between this potential difference and the current in the circuit? Your response differs from the correct answer by more than 10%. Double check your calculations. What are the maximum potential difference across the resistor and the phase angle between this potential difference and the current in this circuit? What are the maximum potential difference across the capacitor and the phase angle between this potential difference and the current in this circuit?

Explanation / Answer

a)

given

R = 289 ohms

C = 46.4 micro F

= 772 mH

Vmax = 120 volts

at f = 50 hz,

Inductive reactance, XL = 2*pi*f*L = 2*pi*50*0.772 = 242.5 ohms

Capacitive reactance, XC = 1/(2*pi*f*c) = 1/(2*pi*50*46.4*10^-6) = 68.6 ohms

Impedance , z = sqrt(R^2 + (XL - XC)^2)

= sqrt(289^2 + (242.5 - 68.6)^2 )

= 337.3 ohms

Imax = Vmax/z

= 120/337.3

= 0.356 A

phase angle, phi = tan^-1( (XL - Xc)/R)

= tan^-1( (242.5 - 68.6)/289)

= 31 degrees

b) VL,max = XL*Imax

= 242.5*0.356

= 86.33 volts

phi = 90 degrees

c) VRmax = R*Imax

= 289*0.356

= 102.9 volts

phi = 0 degrees

d) VCmax = XC*Imax

= 68.6*0.356

= 24.4 volts

phi = 90 degrees

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