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Current Question (ID: 20565)

Question:

$\text{An ideal capacitor of capacitance } 0.2 \, \mu\text{F is charged to a potential difference of } 10 \, \text{V.}$ $\text{The charging battery is then disconnected.}$ $\text{The capacitor is connected to an ideal inductor of self inductance } 0.5 \, \text{mH.}$ $\text{The current at a time when the potential difference across the capacitor is } 5 \, \text{V is:}$

Options:

1. $0.15 \, \text{A}$
2. $0.17 \, \text{A}$
3. $0.34 \, \text{A}$
4. $0.25 \, \text{A}$

Solution:

$\text{Hint: } U = \frac{1}{2} LI^2$

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
}