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NEET Physics Alternating Current / प्रत्यावर्ती धारा NEET PYQ-Alternating Current

  • question_answer
    In an electrical circuit R, L, C and an AC 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                                     [AIPMT (S) 2012]

    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 \[\cos \phi =1\].


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