Import Question JSON

Current Question (ID: 20279)

Question:

$\text{A current of } 5 \text{ A passes through a copper conductor (resistivity=} 1.7 \times 10^{-8} \, \Omega \text{m) of radius of cross-section } 5 \, \text{mm.}$ $\text{Find the mobility of the charges if their drift velocity is } 1.1 \times 10^{-3} \, \text{m/s.}$

Options:

1. $1.0 \, \text{m}^2/\text{Vs}$
2. $1.8 \, \text{m}^2/\text{Vs}$
3. $1.5 \, \text{m}^2/\text{Vs}$
4. $1.3 \, \text{m}^2/\text{Vs}$

Solution:

$\text{Hint: } \mu = \frac{v_d}{E}$ $p = \frac{m}{ne^2\tau} = \frac{1}{ne\mu}$ $i = neA \, v_d$ $n = \frac{i}{eAv_d}$ $\mu = \frac{Av_d}{ip}$ $= \frac{1.1 \times 10^{-3} \times \pi \times 25 \times 10^{-6}}{5 \times 1.7 \times 10^{-8}}$ $= \frac{17.27 \times 10^{-1}}{1.7} \approx 1.0 \, \text{m}^2/\text{Vs}$

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
}