Import Question JSON

Current Question (ID: 17394)

Question:

$\text{A larger parallel plate capacitor, whose plates have an area of } 1 \text{ m}^2, \text{ separated from each other by } 1 \text{ mm, is being charged at a rate of } 25.8 \text{ V/s. If the plates have a dielectric constant } 10, \text{ then the displacement current at this instant is:}$ $1. \ 25 \ \mu\text{A}$ $2. \ 11 \ \mu\text{A}$ $3. \ 2.2 \ \mu\text{A}$ $4. \ 1.1 \ \mu\text{A}$

Options:

1. $25 \ \mu\text{A}$
2. $11 \ \mu\text{A}$
3. $2.2 \ \mu\text{A}$
4. $1.1 \ \mu\text{A}$

Solution:

$\text{Hint: } i_d = C \frac{dV}{dt}$ $\text{Step: Find the displacement current at this instant.}$ $\text{During the charging of the capacitor,}$ $\text{The conduction current = The displacement current}$ $\frac{dQ}{dt} = i_d$ $\Rightarrow Q = CV$ $i_d = C \frac{dV}{dt}$ $i_d = \frac{KA\varepsilon_0}{d} \frac{dV}{dt}$ $i_d = \frac{10 \times 1 \times 8.85 \times 10^{-12}}{10^{-3}} \times 25.8$ $\Rightarrow i_d = 2.28 \ \mu\text{A}$ $\text{Hence, option (3) is the correct answer.}$

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
}