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, \[\cos \,\phi =0.80\]You need to login to perform this action.
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