Answer to Question #128009 in Electric Circuits for Alexandra G Castellanos

Question #128009
A generator connected to an RLC circuit has an rms voltage of 150 V and an rms current of 38 mA .
If the resistance in the circuit is 3.1 kΩ and the capacitive reactance is 6.8 kΩ , what is the inductive reactance of the circuit?
Express your answers using two significant figures. Enter your answers numerically separated by a comma.
(more than one answer)
answer in units of kΩ.
1
Expert's answer
2020-08-02T15:08:35-0400

The Ohm's law says

"I=\\frac{V}{Z}"

Hence, the impedance

"Z=\\frac{V}{I}=\\frac{150\\:\\rm V}{0.038\\:\\rm A}=3942.4\\:\\Omega=3.9\\: k\\Omega"

Also we have

"Z=\\sqrt{R^2+(X_L-X_C)^2}"

So, the inductive reactance of the circuit

"X_L=X_C\\pm\\sqrt{Z^2-R^2}\\\\\n=6.8\\pm\\sqrt{3.9^2-3.1^2}=9.2\\: k\\Omega, 4.4\\: k\\Omega"

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