Import Question JSON

Current Question (ID: 20654)

Question:

$\text{A displacement current of } 4.425 \, \mu\text{A is developed in the space between the plates of a parallel plate capacitor when voltage is changing at a rate of } 10^6 \, \text{V/s.}$ $\text{The area of each plate of the capacitor is } 40 \, \text{cm}^2.$ $\text{The distance between each plate of the capacitor is } x \times 10^{-3} \, \text{m.}$ $\text{The value of } x \text{ is:}$ $\text{(the permittivity of free space, } \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2\text{N}^{-1}\text{m}^{-2})$

Options:

1. $2$
2. $4$
3. $6$
4. $8$

Solution:

$\text{Hint: The displacement current is equal to the conduction current}$ $\text{Step: Find the distance between the plates of the capacitor.}$ $\text{The displacement current is given by;}$ $\Rightarrow \ I_d = \frac{dq}{dt} = C \frac{dV}{dt}$ $\Rightarrow \ I_d = \frac{\varepsilon_0 A}{d} \frac{dV}{dt}$ $\text{Substitute the known values we get;}$ $d = \frac{8.85 \times 10^{-12} \times 4 \times 10^{-3} \times 10^6}{4.425 \times 10^{-6}}$ $\Rightarrow \ d = 8 \, \text{mm} = 8 \times 10^{-3} \, \text{m}$ $\Rightarrow \ x = 8$ $\text{Hence, option (4) is the correct answer.}$

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
}