Import Question JSON

Current Question (ID: 20486)

Question:

$\text{A 20 Henry inductor and coil is connected to a 10 } \Omega \text{ resistance in series as shown in the figure.}$ $\text{The time at which the rate of dissipation of energy (Joule's heat) across the resistance is equal to the rate at which magnetic energy is stored in the inductor, is:}$

Options:

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

Solution:

$\text{Hint: } \varepsilon = -L \frac{di}{dt}$ $iR = \tau \frac{di}{dt} = \frac{di}{dt/T} = \frac{i}{T}$ $e^{-t/T} = 1 - e^{-t/T}$ $2e^{-t/T} = 1$ $t = T \ln 2$ $T = \frac{L}{R} = \frac{20}{10} = 2$ $t = 2 \ln 2$

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
}