Import Question JSON

Current Question (ID: 16594)

Question:

$\text{A capacitor of } 2 \, \mu\text{F is charged as shown in the figure. When the switch } S \text{ is turned to position 2, the percentage of its stored energy dissipated is:}$

Options:

1. $20\%$
2. $75\%$
3. $80\%$
4. $0\%$

Solution:

$\text{Consider the given figure, When the switch } S \text{ is connected to point 1, then initial energy stored in the capacitor can be given as}$ $= \frac{1}{2} (2\, \mu\text{F}) \times V^2$ $\text{When the switch } S \text{ is connected to point 2, energy dissipated on connection across } 8\, \mu\text{F will be}$ $= \frac{1}{2} \left( \frac{C_1 C_2}{C_1 + C_2} \right) V^2$ $= \frac{1}{2} \times \frac{2\, \mu\text{F} \times 8\, \mu\text{F}}{10} \times V^2$ $= \frac{1}{2} \times (1.6\, \mu\text{F}) \times V^2$ $\text{Therefore, } \% \text{ loss of energy } = \frac{1.6}{2} \times 100 = 80\%$

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
}