Alternating Current - Result Question 26
26. 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 volt. The power factor of the circuit is [2006]
(a) 0.64
(b) 0.80
(c) 0.33
(d) 0.56
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Answer:
Correct Answer: 26. (b)
Solution:
(b) Power factor, $\phi=\frac{R}{\sqrt{(\omega L-\frac{1}{\omega C})^{2}+R^{2}}}$
$ =\frac{8}{\sqrt{(31-25)^{2}+8^{2}}}=\frac{8}{\sqrt{6^{2}+8^{2}}}=\frac{8}{10}=0.8 $
Power factor $=\cos \theta=\frac{R}{Z}$
For purely inductive and purely capacitive circuits, $\theta=90^{\circ}$
Power factor $=\cos \theta=\cos 90^{\circ}=\theta$ For non-inductive circuit, $\theta=0^{\circ}$ $\cos \theta=\cos 0^{\circ}=1$
