A) 1/2
B) \[1/\sqrt{2}\]
C) 1
D) \[\sqrt{3}/2\]
Correct Answer: C
Solution :
Here, phase difference \[\tan \phi =\frac{{{X}_{L}}-{{X}_{C}}}{R}\] \[\tan \frac{\pi }{3}=\frac{{{X}_{L}}-{{X}_{C}}}{R}\] When, L is removed \[\sqrt{3}=\frac{{{X}_{C}}}{R}\] \[{{X}_{C}}=\sqrt{3}R\] When C is removed \[\tan \frac{\pi }{3}=\sqrt{3}=\frac{{{X}_{L}}}{R}\] \[{{X}_{L}}=R\sqrt{3}\] Hence, in resonant circuit \[\tan \phi =\frac{\sqrt{3}R=\sqrt{3}R}{R}=0\] \[\phi =0\] \[\therefore \]Power factor \[\cos \phi =1\] It is the condition of resonance therefore phase difference between voltage and current is zero and power factor is \[\cos \phi =1.\]You need to login to perform this action.
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