Import Question JSON

Current Question (ID: 20286)

Question:

$\text{A cylindrical wire of radius } 0.5 \text{ mm and conductivity } 5 \times 10^7 \text{ S/m is subjected to an electric field of } 10 \text{ mV/m. The expected value of current in the wire will be:}$ $1. \ 125\pi \ \text{mA}$ $2. \ 250\pi \ \text{mA}$ $3. \ 325\pi \ \text{mA}$ $4. \ 420\pi \ \text{mA}$

Options:

1. $125\pi \ \text{mA}$
2. $250\pi \ \text{mA}$
3. $325\pi \ \text{mA}$
4. $420\pi \ \text{mA}$

Solution:

$\text{Hint: } J = \sigma E = \frac{i}{A}$ $\text{Conductivity } \sigma = 5 \times 10^7 \text{ S/m}$ $\text{Radius } r = 0.5 \text{ mm} = 5 \times 10^{-4} \text{ m}$ $E = 10 \times 10^{-3} \frac{\text{V}}{\text{m}}$ $J = \sigma E = 10^{-3} \times 5 \times 10^7$ $J = 5 \times 10^5$ $\frac{i}{A} = 5 \times 10^5$

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
}