Consider the circuit shown. The switch is closed at t = 0. Currents in various branches are marked. Which of the following is correct?

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At $t = 0, I_{1} = \frac{E}{3 R}, I_{3} = \frac{E}{3 R}$

At $t = 0, I_{1} = \frac{E}{3 R}, I_{2} = \frac{E}{6 R}, I_{3} = \frac{E}{3 R}$

As $t \to \infty, I_{1} = \frac{E}{2 R}, I_{2} = \frac{E}{4 R}, I_{3} = \frac{E}{4 R}$

As $t \to \infty, I_{1} = \frac{E}{2 R}, I_{2} = \frac{E}{2 R}$

answer is B, D.

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Detailed Solution

At $t = 0, I_{2} = 0 and I_{3} = \frac{E}{3 R}$

$\Rightarrow I_{1} = I_{2} + I_{3} = \frac{E}{3 R}$

As $t \to \infty, I_{3} = 0, I_{2} = \frac{E}{2 R}$

$\Rightarrow I_{1} = I_{2} + I_{3} = \frac{E}{2 R}$

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