Import Question JSON

Current Question (ID: 20201)

Question:

$\text{When } 5 \text{ V potential difference is applied across a wire of length } 0.1 \text{ m, the drift speed of electrons is } 2.5 \times 10^{-4} \text{ ms}^{-1}. \text{ If the electron density in the wire is } 8 \times 10^{28} \text{ m}^{-3}, \text{ the resistivity of the material is close to:}$

Options:

1. $1.6 \times 10^{-8} \ \Omega\text{-m}$
2. $1.6 \times 10^{-7} \ \Omega\text{-m}$
3. $1.6 \times 10^{-6} \ \Omega\text{-m}$
4. $1.6 \times 10^{-5} \ \Omega\text{-m}$

Solution:

$\text{Hint: } I = neAv_d$ $\text{E} = \rho J$ $\frac{V}{l} = \rho ne v_d$ $\rho = \frac{V}{lne v_d}$ $= \frac{5}{0.1 \times 8 \times 10^{28} \times 1.6 \times 10^{-19} \times 2.5 \times 10^{-4}}$ $= 0.156 \times 10^{-4}$ $= 1.56 \times 10^{-5}$ $= 1.6 \times 10^{-5} \ \Omega\text{m}$

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
}