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NEET AIPMT SOLVED PAPER SCREENING 2006

  • question_answer
                    A coil of inductive reactance \[31\,\,\Omega \]. has a resistance of \[8\,\,\Omega \]. It is placed in series with a condenser of capacitative reactance \[25\,\,\Omega \]. The combination is connected to an a.c. source of 110 V. The power factor of the circuit is:                                                                                                                                                               

    A)                  0.56              

    B)                  0.64                      

    C)                  0.80     

    D)                  0.33

    Correct Answer: C

    Solution :

                    Key Idea: Power factor \[(\cos \phi )\] is a ratio of resistance and impedance of AC circuit. Power factor of AC circuit is given by                 \[\cos \phi =\frac{R}{Z}...(i)\]                 where R is resistance employed and Z the impedance of the circuit.                 \[Z=\sqrt{{{R}^{2}}+({{X}_{L}}+X_{C}^{2})}\]       ...(ii)                 Eqs. (i) and (ii) meet to give,                 \[\cos \phi =\frac{R}{\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{X}_{C}})}^{2}}}}....(iii)\]                 Given,  \[R=8\Omega ,\,\,{{X}_{L}}=31\,\Omega ,\,\,{{X}_{C}}=25\,\Omega \]                 \[\therefore \cos \phi =\frac{8}{\sqrt{{{(8)}^{2}}+{{(31-25)}^{2}}}}\]                 \[=\frac{8}{\sqrt{64+36}}\]                 Hence,  \[\cos \,\phi =0.80\]


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