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  • A series LCR circuit is connected to an AC source of  <img alt="220 \mathrm{~V}, 50 \mathrm{~Hz}" src="https://entrancecorner.oncodecogs.com/gif.latex?220%20%5Cmathrm%7B%7EV%7D%2C%2050%20%5Cma

A series LCR circuit is connected to an AC source of  220 \mathrm{~V}, 50 \mathrm{~Hz}. The circuit contains a resistance \mathrm{R}=$ $80 \Omega, an inductor of inductive reactance \mathrm{X}_{\mathrm{L}}=70 \Omega, and a capacitor of capacitive reactance \mathrm{X}_{\mathrm{C}}=130 \Omega. The power factor of circuit is \frac{x}{10}. The value ofx is:

Option: 1

8


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} & \cos \phi=\frac{R}{Z}=\frac{\mathrm{R}}{\sqrt{\mathrm{R}^2+\left(X_C-X_L\right)^2}} \\ & =\frac{80}{\sqrt{(80)^2+(130-70)^2}}=\frac{80}{\sqrt{(80)^2+(60)^2}} \\ & \cos \phi=\frac{80}{100}=\frac{8}{10} \\ & \mathrm{x}=8 \end{aligned}

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