Import Question JSON

Current Question (ID: 17036)

Question:

$\text{The network shown in figure is a part of a complete circuit. If at a certain instant, the current } i \text{ is } 10 \text{ A and is increasing at the rate of } 4 \times 10^3 \text{ A/sec, then } V_A - V_B \text{ is:}$

Options:

1. $6 \text{ V}$
2. $-6 \text{ V}$
3. $10 \text{ V}$
4. $-10 \text{ V}$

Solution:

$\text{Since current is increasing, inductor will decrease current}$ $\text{For inductor,}$ $\mathcal{E}_{\text{ind}} = L \frac{di}{dt}$ $= 10^{-3} \times 4 \times 10^3$ $= 4 \text{ V}$ $V_A - V_B = -4 + 20 - 1 \times 10$ $= 6 \text{ V}$

Import JSON File

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
}