Import Question JSON

Current Question (ID: 16584)

Question:

$\text{Two condensers, one of capacity } C \text{ and the other of capacity } \frac{C}{2} \text{ are connected to a } V \text{ volt battery, as shown in the figure.}$ $\text{The energy stored in the capacitors when both condensers are fully charged will be:}$

Options:

1. $2CV^2$
2. $\frac{1}{4}CV^2$
3. $\frac{3}{4}CV^2$
4. $\frac{1}{2}CV^2$

Solution:

$\text{Hint: } U = \frac{1}{2}CV^2$ $\text{Step: Find the energy stored in the capacitors.}$ $\text{In the circuit, two capacitors } (C, \frac{C}{2}) \text{ are in parallel configuration with a battery } V.$ $\text{Then, } C_{\text{eff}} = C + \frac{C}{2} = \frac{3}{2}C$ $\text{Therefore, the energy stored in the capacitors is given by:}$ $U = \frac{1}{2}C_{\text{eff}}V^2 = \frac{1}{2}\left(\frac{3C}{2}\right)V^2$ $\Rightarrow U = \frac{3}{4}CV^2$ $\text{Hence, option (3) is the correct answer.}$

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
}