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