An AC power source has an rms voltage of 1.20 ? 10 2 V and operates at a frequen

Question

An AC power source has an rms voltage of 1.20 ? 102 V and operates at a frequency of 60 Hz. If a series RLC circuit is made from the power source, a 0.780 ?F capacitor, a 15.0 H inductor and a 2.10 ? 103 ? 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
A

Explanation / Answer

a) capacitance reactance XC = 1 / 2 pi f C

= 1 / ( 2 pi * 60 * 0.780 * 10-6 ) = 3400 ohm

b) Inductive reactance XL = 2 pi f L

= 2 pi * 60 * 15 = 5655 ohm

c) impedance = sqrt ( R2 + ( XL - XC )2 )

= sqrt( 21002 + (5655 - 3400)2 ) = 3081 ohm

d) Maximum current I = V / Z

= 120 / 3081 = 0.039 A

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