Import Question JSON

Current Question (ID: 20154)

Question:

$\text{Find energy stored in capacitor in given circuit.}$

Options:

1. $0.2 \text{ mJ}$
2. $0.4 \text{ mJ}$
3. $0.6 \text{ mJ}$
4. $0.8 \text{ mJ}$

Solution:

$\text{Hint: In a steady state, the capacitor will behave as an open circuit.}$ $R_{\text{eq}} = 4 \Omega$ $i = \frac{12}{4} = 3 \text{ A}$ $i_4 = \frac{12}{18} \times 3 = 3 \text{ A}$ $i_3 = 1 \text{ A}$ $\text{So, P.D. across capacitor}$ $-3-V+8=0$ $V = 5 \text{ volt}$ $\text{Energy stored} = \frac{1}{2} CV^2$ $= \frac{1}{2} \times 16 \text{ (}\mu\text{C)} \times 25$ $= 200 \mu\text{J}$

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
}