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  4. A coil of inductive reactance 31 Ω has a resistance of 8 Ω. It is placed in series with a condenser of capacitive reactance 25Ω. The combination is connected to an ac source of 110 V . The power factor of the circuit is

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Q. A coil of inductive reactance 31 Ω has a resistance of 8 Ω. It is placed in series with a condenser of capacitive reactance 25Ω. The combination is connected to an ac source of 110 V . The power factor of the circuit is

NTA AbhyasNTA Abhyas 2020

Solution:

$X_{L}=31 \Omega, X_{C}=25 \Omega, R=8 \Omega$
Impedance of series $L C R$ is
$\mathrm{Z}=\sqrt{\left(\mathrm{R}^{2}\right)+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^{2}}$
$=\sqrt{(8)^{2}+(31-25)^{2}}=\sqrt{64+36}=10 \Omega$
Power factor, $\cos \phi=\frac{R}{Z}=\frac{8}{10}=0.8$