Question

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

• A. $0.33$
• B. $0.56$
• C. $0.64$
• D. $0.80$

Answer 1

Answer: (D)

$X _{ L }=31 \, \Omega, x _{ C }=25\, \Omega, R =8 \, \Omega$
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, $\cos \phi=\frac{ R }{ z }=\frac{8}{10}=0.8$