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  • Stuck here, help me understand: - Electromagnetic Induction and alternative Currents - NEET

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 \frac{\pi}{3}. If instead, C is removed from the circuit, the phase difference is again \frac{\pi}{3}. The power factor of the circuit is:

  • Option 1)

    \frac{1}{2}

  • Option 2)

    \frac{1}{\sqrt2}

  • Option 3)

    1

  • Option 4)

    \frac{\sqrt3}{2}

 

Answers (1)

As we learnt in

Impedence -

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

-

 

 

Power factor -

cos phi = frac{R}{Z}
 

- wherein

R ightarrow resistance

Z ightarrow 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


Option 1)

\frac{1}{2}

Incorrect

Option 2)

\frac{1}{\sqrt2}

Incorrect

Option 3)

1

Correct

Option 4)

\frac{\sqrt3}{2}

Incorrect

Posted by

Vakul

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