A) 0.56
B) 0.64
C) 0.80
D) 0.33
Correct Answer: C
Solution :
Power factor of (AC) circuit is given by \[\phi =\frac{R}{Z}\] ??..(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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