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  • A series of LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is 

A series of LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is \frac{\pi}{3} If instead C is removed from the circuit, the phase difference is again \frac{\pi}{3}  between current and voltage. The power factor of the circuit is:

Option: 1

zero 


Option: 2

0.5

 


Option: 3

1.0


Option: 4

-1.0


Answers (1)

best_answer

\begin{aligned} &\text { For only } \mathrm{RC}:\phi_{\mathrm{RC}}=\frac{\pi}{3}\\ &\tan \left(\frac{\pi}{3}\right)=\frac{\mathrm{X}_{\mathrm{c}}}{\mathrm{R}} \Rightarrow \mathrm{X}_{\mathrm{c}}=\sqrt{3} \mathrm{R}\\ &\text { For only } \mathrm{RL}:\phi_{\mathrm{RL}}=\frac{\pi}{3}\\ &\tan \left(\frac{\pi}{3}\right)=\frac{\mathrm{X}_{\mathrm{L}}}{\mathrm{R}} \Rightarrow \mathrm{X}_{\mathrm{L}}=\sqrt{3} \mathrm{R}\\ &\text { For RL:- }\\ &\tan (\phi)=\frac{\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}}{\mathrm{R}}=\frac{\sqrt{3} \mathrm{R}-\sqrt{3} \mathrm{R}}{\mathrm{R}}=0 \Rightarrow \phi=0 \Rightarrow \cos \phi=1 \end{aligned}

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