A series RLC circuit contains the following components: R = 200 , L = 0.300 H, C

Question

A series RLC circuit contains the following components: R = 200 , L = 0.300 H, C = 2.40 µF, and a source with Vmax = 220 V operating at 40.0 Hz. Our goal is to find the phase angle, the power factor, and the power input for this circuit.

(a) Find the inductive reactance in the circuit. (k)
(b) Find the capacitive reactance in the circuit. (k)
(c) Find the impedance in the circuit. (k)
(d) Calculate the maximum current in the circuit. (mA)
(e) Determine the phase angle between the current and source voltage. (°)
(f) Find the power factor for the circuit.
(g) Find the power input to the circuit. (W)

Explanation / Answer

inductive reactance XL = L*w = 0.3* 2pi * 40 = 75.398 = 0.0753982237 k

capacitive reactance = 1/cw = 1/ ( 2.40*10^-6 * 2*pi * 40) =1.65786399 k   

impedance Z = sqrt{ ( 1.65786399-0.0753982237 )^2 + 0.2^2 } = 1.595 k

max current = V/R = 220 / 200 = 1.1 A = 1100 mA

phase angle = atan { ( XC-Xr) / R}

= atan( ( 1.65786399-0.0753982237)/ 0.2) = 82.79 degree

voltage behind the currrent

power factor = cos(  82.79) = 0.125

power input = V*I = 220* 1.1 /2 = 121 *0.125 =15.125 W

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