Import Question JSON

Current Question (ID: 20128)

Question:

$\text{Two capacitors of capacitances } C \text{ and } 2C \text{ are charged to potential differences } V \text{ and } 2V, \text{ respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:}$

Options:

1. $\frac{9}{2}CV^2$
2. $\frac{25}{6}CV^2$
3. $\text{zero}$
4. $\frac{3}{2}CV^2$

Solution:

$\text{Hint: } E = \frac{1}{2}CV^2$ $Q_1 = CV$ $Q_2 = 2C \times 2V = 4CV$ $\Rightarrow \text{By conservation of charge}$ $q_i = q_f$ $Q_1 + Q_2 = q_1 + q_2$ $4CV - CV = (C + 2C) V_c$ $V_c = \frac{3CV}{3C} \Rightarrow V_c = V$ $\Rightarrow \frac{1}{2} \times (3C) \times V_c^2$ $= \frac{1}{2} \times 3C \times V^2 = \frac{3}{2}CV^2$

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
}