JEE Main & Advanced Sample Paper JEE Main Sample Paper-29

  • question_answer
    In the given circuit diagram, the key K is switched on at \[t=0\]. The ratio of the current i through the cell at \[t=0\] and \[t=\infty \] will be :

    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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