Import Question JSON

Current Question (ID: 20251)

Question:

$\text{A conductor of length } l \text{ and cross-sectional area } A \text{ has drift velocity } v_d$ $\text{when used across a potential difference } V.$ $\text{When another conductor of the same material and length } l \text{ but}$ $\text{double cross-sectional area than the first, is used across}$ $\text{the same potential difference then drift velocity is equal to:}$

Options:

1. $\frac{v_d}{2}$
2. $v_d$
3. $2v_d$
4. $4v_d$

Solution:

$I = \frac{V}{R} = \frac{V}{\frac{\rho l}{A}} = \frac{VA}{\rho l}$ $neAv_d = \frac{VA}{\rho l}$ $\text{All the parameters remain same except cross sectional area and } v_d$ $\text{is independent of cross-sectional area when compared in two}$ $\text{different conductors so, } v_d \text{ remains same.}$

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
}