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Dipole Moment

Capacitor in ...

Question

Capacitor in the circuit is initially uncharged. Find out current $I_{1}, I_{2}, I_{3}$ after a long time when the switch is closed.

A

I_{1} = \frac{E}{2 R}, I_{2} = 0, I_{3} = \frac{E}{2 R}

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B

I_{1} = \frac{E}{3 R}, I_{2} = \frac{E}{3 R}, I_{3} = \frac{E}{3 R}

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C

I_{1} = \frac{E}{3 R}, I_{2} = \frac{2 E}{3 R}, I_{3} = \frac{E}{3 R}

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D

I_{1} = \frac{2 E}{3 R}, I_{2} = \frac{E}{3 R}, I_{3} = 0

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Solution

The correct option is A $I_{1} = \frac{E}{2 R}, I_{2} = 0, I_{3} = \frac{E}{2 R}$
At $t = \infty$ (finally), capacitor is completely charged. So, their will be no current through it.

So,
$I_{2} = 0,$

Using Ohm's law:

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

Hence, option (a) is the correct answer.

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