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

Question

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.

Answer 1

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

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