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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