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  4. A series LCR circuit is connected to an AC source of 220 V , 50 Hz. The circuit contains a resistance R =80 Ω, an inductor of inductive reactance X L =70 Ω, and a capacitor of capacitive reactance X C =130 Ω. The power factor of circuit is (x/10). The value of x is :

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

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Solution:

$ \cos \phi=\frac{R}{Z}=\frac{ R }{\sqrt{ R ^2+\left( X _{ C }- X _{ L }\right)^2}} $
$ \cos \phi=\frac{80}{\sqrt{(80)^2+(60)^2}} $
$ \cos \phi=\frac{80}{100} \Rightarrow \frac{8}{10}$
So, $x=8$