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Current Question (ID: 17035)

Question:

$\text{The figure shows three circuits with identical batteries, inductors, and resistors. Rank the circuits according to the current, in descending order, through the battery } (i) \text{ just after the switch is closed and } (ii) \text{ a long time later:}$

Options:

1. $(i) \ i_2 > i_3 > i_1 \ (i_1 = 0) \ \ (ii) \ i_2 > i_3 > i_1$
2. $(i) \ i_2 < i_3 < i_1 \ (i_1 \neq 0) \ \ (ii) \ i_2 < i_3 < i_1$
3. $(i) \ i_1 > i_2 > i_3 \ (i_1 \neq 0) \ \ (ii) \ i_1 > i_2 > i_3$
4. $(i) \ i_1 = i_2 = i_3 \ \ (ii) \ i_1 = i_2 = i_3$

Solution:

$\text{(1) Just before closing the switch:}$ $i_1 = 0, \ i_2 = \frac{E}{R}, \ i_3 = \frac{E}{2R}$ $\text{So, } i_2 > i_3 > i_1 \ (i_1 = 0)$ $\text{After a long time closing the switch:}$ $R_{eq} = 2R$ $R_{eq} = \frac{R}{2}$ $R_{eq} = R$ $\text{Hence, } i_2 > i_3 > i_1$

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Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}