Import Question JSON

Current Question (ID: 16716)

Question:

$\text{See the electrical circuit shown in this figure. Which of the following is a correct equation for it?}$

Options:

1. $\varepsilon_1 - (i_1 + i_2)R - i_1r_1 = 0$
2. $\varepsilon_2 - i_2r_2 - \varepsilon_1 - i_1r_1 = 0$
3. $-\varepsilon_2 - (i_1 + i_2)R + i_2r_2 = 0$
4. $\varepsilon_1 - (i_1 + i_2)R + i_1r_1 = 0$

Solution:

$\text{On applying the Kirchhoff's loop law which is based on energy conservation:}$ $\text{The algebraic sum of changes in potential around any closed loop of a circuit must be zero. i.e. } \Sigma IR = 0$ $\text{After analyzing the above circuit we can write the following equation by applying the Kirchhoff's law}$ $\varepsilon_1 - (i_1 + i_2)R - i_1r_1 = 0$

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
}