Import Question JSON

Current Question (ID: 17034)

Question:

$\text{When the current in the portion of the circuit shown in the figure is } 2 \text{ A and increases at the rate of } 1 \text{ A/s, the measured potential difference } V_{ab} = 8 \text{ V.}$ $\text{However, when the current is } 2 \text{ A and decreases at the rate of } 1 \text{ A/s, the measured potential difference } V_{ab} = 4 \text{ V. The value of } R \text{ and } L \text{ is:}$

Options:

1. $3 \, \Omega \text{ and } 2 \, \text{H respectively}$
2. $3 \, \Omega \text{ and } 3 \, \text{H respectively}$
3. $2 \, \Omega \text{ and } 1 \, \text{H respectively}$
4. $3 \, \Omega \text{ and } 1 \, \text{H respectively}$

Solution:

$\text{Using the formula for potential difference across an inductor:}$ $V_{ab} = iR + L \frac{di}{dt}$ $\text{For the first case:}$ $8 = 2R + L \times 1$ $\text{For the second case:}$ $4 = 2R - L \times 1$ $\text{Solving these equations:}$ $8 = 2R + L$ $4 = 2R - L$ $\text{Adding the equations:}$ $12 = 4R \Rightarrow R = 3 \, \Omega$ $\text{Substituting } R \text{ in one of the equations:}$ $8 = 2 \times 3 + L \Rightarrow L = 2 \, \text{H}$

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
}