A) \[\sqrt{3/5}\]
B) \[\sqrt{5/3}\]
C) \[\sqrt{2/3}\]
D) \[\sqrt{3/2}\]
Correct Answer: A
Solution :
[a] According to given problem, \[I\,=\frac{V}{Z}\,=\frac{V}{{{[{{R}^{2}}+{{(1/C\omega )}^{2}}]}^{1/2}}}\] ??.(i) and \[\frac{I}{2}\,=\frac{V}{{{[{{R}^{2}}+{{(3/C\omega )}^{2}}]}^{1/2}}}\] ??.(ii) Substituting the value of I from eq. (i) in (11), \[4\,\left( {{R}^{2}}+\frac{1}{{{C}^{2}}{{\omega }^{2}}} \right)={{R}^{2}}+\frac{9}{{{C}^{2}}\,{{\omega }^{2}}}\] i.e., \[\frac{1}{{{C}^{2}}\,{{\omega }^{2}}}\,=\frac{3}{5}\,{{R}^{2}}\] so that \[\frac{X}{R}\]
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