Import Question JSON

Current Question (ID: 17388)

Question:

$\text{Instantaneous displacement current of } 2.0 \text{ A is set up in the space between two parallel plates of } 1 \ \mu\text{F capacitor. The rate of change in potential difference across the capacitor is:}$

Options:

1. $1.3 \times 10^6 \ \text{V/s}$
2. $4 \times 10^6 \ \text{V/s}$
3. $2 \times 10^6 \ \text{V/s}$
4. $\text{None of these}$

Solution:

$\text{Hint: } I_d = \varepsilon_0 \frac{d\phi_E}{dt} = \varepsilon_0 A \frac{d}{dt} \left( \frac{V}{d} \right)$ $\text{Step: Find the rate of change in potential difference across the capacitor.}$ $I_d = \varepsilon_0 \frac{d\phi_E}{dt} = \varepsilon_0 A \frac{d}{dt} \left( \frac{V}{d} \right)$ $I_d = C \frac{dV}{dt}$ $\text{Substitute the known values we get;}$ $\Rightarrow \frac{dV}{dt} = \frac{2}{10^{-6}} = 2 \times 10^6 \ \text{V/sec}$ $\text{Hence, option (3) is the correct answer.}$

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
}