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 807 mH, a resistance of 234 ohm, and a capacitance of 43.6 mu F (a) What are the maximum current and the phase angle between the current and the source emf in this circuit? I_max = phi = (b) What are the maximum potential difference across the inductor and the phase angle between this potential difference and the current in the circuit? V_L, max = phi = (c) What are the maximum potential difference across the resistor and the phase angle between this potential difference and the current in this circuit? V_R, max = phi = d) What are the maximum potential difference across the capacitor and the phase angle between this potential difference and the current in this circuit? V_C, max = phi =

Explanation / Answer

(a)

capacitive inductance Xc = 1/(wc) = 1/(2*pi*f*C)

Xc = 1/(2*pi*50*43.6*10^-6) = 73 ohm

Inductive reactance = XL = wL = 2*pi*f*L

XL = 2*pi*50*807*10^-3 = 253.5 ohms

impedance Z = sqrt(R^2+(XL-Xc)^2)

Z = sqrt(234^2+(253.5-73)^2) = 295.5 ohm

Imax = Vmax/Z

Imax = 120/295.5 = 0.41 A <<<<----------answer

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

phase = tan^-1((253.5-73)/234) = 37.65 degrees <<<<------answer

=======================

(b)

Vmax = Imax*XL = 0.41*253.5 = 104 V

phase = 90 degrees

====================

(c)

VR = IMax*R = 0.41*234 = 96 V

phase = 0

==================

(d)

VC = Imax*XC = 0.41*73 = 30 V

phase 270

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