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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.

Respuesta :

Answer:

53.06 ohm

Explanation:

We have given the rms voltage V =140 V

And the rms current i=31 mA

So the impedance [tex]Z=\frac{V}{i}=\frac{140}{3\times 10^{-3}}=46.666kohm[/tex]

Resistance is given as R = 3 kohm

And capacitive reactance [tex]X_C=6.5kohm[/tex]

We know that [tex]Z=\sqrt{R^2+(X_L-X_C)^2}[/tex]

[tex]46.666=\sqrt{3^2+(X_L-6.5)^2}[/tex]

Squaring both side [tex]2177.1556=9+(X_L-6.5)^2[/tex]

[tex](X_L-6.5)^2=2168.155[/tex]

[tex](X_L-6.5)=46.5634[/tex]

[tex]X_L=53.063ohm[/tex]

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