Question

A generator connected to an RLC circuit has an rms voltage of 140 V and an rms current of 31 mA. Part A

If the resistance in the circuit is 3.0 kΩ and the capacitive reactance is 6.5 kΩ , what is the inductive reactance of the circuit? Express your answers using two significant figures. Enter your answers numerically separated by a comma.

Answer 1

53.06 ohm

Step-by-step explanation:

We have given the rms voltage V =140 V

And the rms current i=31 mA

So the impedance
`Z=(V)/(i)=(140)/(3* 10^(-3))=46.666kohm`

Resistance is given as R = 3 kohm

And capacitive reactance
`X_C=6.5kohm`

We know that
`Z=√(R^2+(X_L-X_C)^2)`

`46.666=√(3^2+(X_L-6.5)^2)`

Squaring both side
`2177.1556=9+(X_L-6.5)^2`

`(X_L-6.5)^2=2168.155`

`(X_L-6.5)=46.5634`

`X_L=53.063ohm`