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 and 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:

As we learnt in

Impedence -

$Z= \sqrt{R^{2}+\left ( \omega L -\frac{1}{\omega c}\right )^{2}}$

-

Power factor -

$\cos \phi = \frac{R}{Z}$

- wherein

$R\rightarrow$ resistance

$Z\rightarrow$ impedence

$\frac{Xc}{R}= \tan \frac{\pi }{3}\Rightarrow X_{c}=R \tan \frac{\pi }{3}$

when C is removed from the Circuit

$\frac{X_{L}}{R}= \tan \frac{\pi }{3}\Rightarrow X_{L}=R \tan \frac{\pi }{3}$

$Z= \sqrt {R^{2}+\left ( X_{L}-X_{C} \right )^{2}} =Z=R$

Power factor $\cos \phi = \frac{R}{z}=\frac{z}{z}=1$

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