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

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A

$0.33$

B

$0.56$

C

$0.64$

D

$0.80$

Solution:

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

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