A) \[3:1\]
B) \[1:3\]
C) \[1:2\]
D) \[2:1\]
Correct Answer: D
Solution :
AT t = 0, capacitor acts as a pure conductor. The effective resistance of the circuit is R and current \[A+B+C=\pi \Rightarrow B={{60}^{\text{o}}}\] At \[\frac{\sin B}{\sin C}=\frac{\sqrt{3}}{\sqrt{2}}=\frac{\sqrt{3}}{2}.\,\frac{1}{\sin C}\] capacitor acts as a pure insulator and inductor acts as a pure conductor. The effective resistance of the circuit is \[\sin C=\frac{1}{\sqrt{2}}\Rightarrow \,C={{45}^{\text{o}}}\,\Rightarrow \,A={{75}^{\text{o}}}\] and the current \[\frac{dy}{dx}=2x\,-\frac{1}{{{x}^{2}}}\Rightarrow \,y={{x}^{2}}\,+\frac{1}{x}+c\] \[M(-1,\,1)\,\Rightarrow \,1=1-1\,+c\Rightarrow \,c=1\]
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