Alternating Current Question 5
Question 5 - 25 January - Shift 2
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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Answer: (8)
Solution:
Formula: Some Definitions
$\cos \phi=\frac{R}{Z}=\frac{R}{\sqrt{R^{2}+\left(X_{C}-X_{L}\right)^{2}}}$
$\cos \phi=\frac{80}{\sqrt{(80)^{2}+(60)^{2}}}$
$\cos \phi=\frac{80}{100} \Rightarrow \frac{8}{10}$
