https://session.masteringphysics.com/problemAsset/1013176/14/1013176.jpg An L-R-
ID: 1366579 • Letter: H
Question
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An L-R-C circuit, operating at 60 Hz, has an inductor with an inductance of 1.53×103H, a capacitance of 1.67×102F, and a resistance of 0.329 . What is the inductive reactance of this circuit?
What is the capacitive reactance of this circuit?
What is the total impedance of the circuit?
If this circuit were connected to a standard 120 V ac outlet, what would the rms current in the circuit be?
To see whether the L-R-C ac circuit from Part A would be suitable for a tuner in a radio, find the resonant frequency of this circuit.
Explanation / Answer
inductive reactance is
XL = 2 pi fL = 2 pi ( 60 Hz) ( 1.53 * 10 ^-3 H) = 0.576 ohm
capacitive reactance
XC = 1/ 2 pi fc = 1/ 2pi ( 60 ) ( 1.67 ^ 10 ^-2 F)
=0.158 ohm
impedence is
z = root R^2 + (XL - XC)^2
= root ( 0.329)^2 + ( 0.576 -0.158)^2
=0.531 ohm
rms current is
Irms=Vrms/Z=120/0.532=226A
f = 1/2pi root LC
= 1/ 2 pi root (1.53 * 10 ^-3 H) ( 1.67 * 10 ^-2 F)
= 31.5 Hz
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