Electro Magnetic Induction And Alternating Currents Question 199
Question: In an electrical circuit R, L, C and an a.c. voltage source are all connected in series. When L is removed from the circuit, the phase difference between the voltage the current in the circuit is $ \pi /3 $ . If instead, C is removed from the circuit, the phase difference is again $ \pi /3 $ . The power factor of the circuit is :
Options:
A) $ 1/2 $
B) $ 1/\sqrt{2} $
C) 1
D) $ \sqrt{3}/2 $
Show Answer
Answer:
Correct Answer: C
Solution:
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when L is removed from the circuit
$ [ \because R=\frac{V}{I}=\frac{80}{10}=8 ] $
$ X_{C}=R,\tan ,\frac{\pi }{3} $ –(i)
when C is remove from the circuit
$ \frac{X_{L}}{R}=\tan ,\frac{\pi }{3} $
$ X_{C}=R,\tan ,\frac{\pi }{3} $ …(ii)
net impedence $ Z=\sqrt{R^{2}+(X_{L}-X_{C})}=R $
power factor cos $ \phi ,=\frac{R}{Z}=1 $
