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Current Question (ID: 20488)

Question:

$\text{A coil of self inductance } 10 \ \text{mH} \text{ and resistance } 0.1 \ \Omega \text{ is connected through a switch to a battery of internal resistance } 0.9 \ \Omega. \text{ After the switch is closed, the time taken for the current to attain } 80\% \text{ of the saturation value is: [take } \ln 5 = 1.6]$

Options:

1. $0.324 \ \text{s}$
2. $0.002 \ \text{s}$
3. $0.103 \ \text{s}$
4. $0.016 \ \text{s}$

Solution:

$i = i_0 \left[ 1 - e^{-\frac{Rt}{L}} \right]$ $0.8 \ i_0 = i_0 \left[ 1 - e^{-\frac{Rt}{L}} \right]$ $e^{-\frac{Rt}{L}} = 0.2 = \frac{1}{5}$ $-\frac{Rt}{L} = -\ln(5)$ $t = \frac{L}{R} \ln(5)$ $= 0.016 \ \text{sec}$

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
}