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A coil of inductive reactance $31 \Omega$ has a resistance of $8 \Omega$. It is placed in series with a condenser of capacitative reactance $25 \Omega$. The combination is connected to an a.c. source of $110 \mathrm{~V}$. The power factor of the circuit is:
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Verified Answer
The correct answer is:
0.80
$X_L=31 \Omega, X_C=25 \Omega, R=8 \Omega$
$\therefore$ impedance of series LCR is
$$
\begin{aligned}
& \mathrm{Z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2} \\
& =\sqrt{8^2+(31-25)^2} \\
& =\sqrt{64+36}=\sqrt{100}=10 \Omega
\end{aligned}
$$
Power factor
$$
\cos \phi=\frac{R}{2}=\frac{8}{10}=0.8
$$
$\therefore$ impedance of series LCR is
$$
\begin{aligned}
& \mathrm{Z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2} \\
& =\sqrt{8^2+(31-25)^2} \\
& =\sqrt{64+36}=\sqrt{100}=10 \Omega
\end{aligned}
$$
Power factor
$$
\cos \phi=\frac{R}{2}=\frac{8}{10}=0.8
$$
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