Import Question JSON

Current Question (ID: 17386)

Question:

$\text{A capacitor is having a capacity of } 2 \text{ pF.}$ $\text{The electric potential across the capacitor is changing with a value of } 10^{12} \text{ V/s.}$ $\text{The displacement current is:}$

Options:

1. $2 \text{ A}$
2. $3 \text{ A}$
3. $6 \text{ A}$
4. $9 \text{ A}$

Solution:

$\text{Hint: } i_D = C \frac{dV}{dt}$ $\text{Step: Find the displacement current in the capacitor.}$ $\text{The displacement current in the capacitor is given by;} \ i_D = C \frac{dV}{dt}$ $\text{Substitute the known values we get;} \ \Rightarrow i_D = 2 \times 10^{-12} \times 10^{12} = 2 \text{ A}$ $\text{Hence, option (1) is the correct answer.}$

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
}