A) \[\sqrt{\frac{2}{3}}\]
B) \[\sqrt{\frac{2}{5}}\]
C) \[\sqrt{\frac{3}{2}}\]
D) \[\sqrt{\frac{5}{2}}\]
Correct Answer: D
Solution :
Power factor \[\text{(old)}\] \[=\frac{R}{\sqrt{{{R}^{2}}+{{X}_{L}}^{2}}}=\frac{R}{\sqrt{{{R}^{2}}+{{(2R)}^{2}}}}=\frac{R}{\sqrt{5}R}\] Power factor\[_{(new)}\] \[=\frac{R}{\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{X}_{C}})}^{2}}}}=\frac{R}{\sqrt{{{R}^{2}}+{{(2R-R)}^{2}}}}\]\[=\frac{R}{\sqrt{2}R}\] \[\therefore \]\[\frac{\text{New}\,\text{power}\,\text{factor}}{\text{Old}\,\text{power}\,\text{factor}}=\frac{\frac{R}{\sqrt{2}R}}{\frac{R}{\sqrt{5}R}}=\sqrt{\frac{5}{2}}\]
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