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=VZI=\frac{V}{Z}

Hence, the impedance

Z=VI=150V0.038A=3942.4Ω=3.9kΩZ=\frac{V}{I}=\frac{150\:\rm V}{0.038\:\rm A}=3942.4\:\Omega=3.9\: k\Omega

Also we have

Z=R2+(XLXC)2Z=\sqrt{R^2+(X_L-X_C)^2}

So, the inductive reactance of the circuit

XL=XC±Z2R2=6.8±3.923.12=9.2kΩ,4.4kΩX_L=X_C\pm\sqrt{Z^2-R^2}\\ =6.8\pm\sqrt{3.9^2-3.1^2}=9.2\: k\Omega, 4.4\: k\Omega

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