An AC power source has an rms voltage of 1.20 X 10 V and operates at a frequency

Question

An AC power source has an rms voltage of 1.20 X 10 V and operates at a frequency of 60 Hz. If a series RLC circuit is mede from the power source, a 0.860 capacitor, a 15.0 H inductor and a 2.10 X 10, resistor, determine the capacitive reactance, the inductive reactance, the circuit impedance, and the maximum current in the circuit. (a) the capacitive reactance (Enter your answer to at least 3 significant figures.) (b) the inductive reactance (Enter your answer to at least 3 significant figures.) (c) the circuit impedance (d) the maximum current

Explanation / Answer

here,

Vrms = 120 V

frequency , f = 60 Hz

capacitance , C = 0.86 uF = 8.6 * 10^-7 F

inductance , L = 15 H

resistance , R = 2100 ohm

a)

the capacitive resistance , Xc = 1/(2 * pi * f * C)

Xc = 1/ ( 2 * pi * 60 * 8.6 * 10^-7) ohm

Xc = 3086 ohm

b)

the inductive resistance , Xl = 2 * pi * f * L

Xl = 2 * pi * 60 * 15 ohm

Xl = 5652 ohm

c)

the circuit impedance , Z = sqrt(R^2 + ( Xl - Xc)^2)

Z = sqrt(2100^2 + ( 5652 - 3086)^2 )

Z = 3315.8 ohm

d)

the rms current , Irms = Vrms /Z

Irms = 120 /3315.8 = 3.62 * 10^-2 A

the maximum current , Im = Irms * sqrt(2)

Im = 5.2 * 10^-2 A

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