Import Question JSON

Current Question (ID: 17040)

Question:

$\text{Switch } S \text{ of the circuit shown in the figure is closed at } t = 0. \text{ If } e \text{ denotes the induced emf in } L \text{ and } i \text{ denotes the current flowing through the circuit at time } t, \text{ then which of the following graphs is correct?}$

Options:

1. $\text{Graph of } e \text{ vs. } t \text{ showing exponential increase}$
2. $\text{Graph of } i \text{ vs. } t \text{ showing constant current}$
3. $\text{Graph of } e \text{ vs. } t \text{ showing exponential decrease}$
4. $\text{Graph of } i \text{ vs. } t \text{ showing constant current}$

Solution:

$\text{In an L-R circuit, current } i \text{ and induced emf } e \text{ in the inductor are given as:}$ $i = \frac{E}{R} \left(1 - e^{-tR/L}\right)$ $e = E_0 e^{-tR/L}$ $\text{At } t=0, i=0, e=E$ $\text{At } t=\infty, i = \frac{E}{R}, e=0$ $\text{As the time passes, the current through the circuit increases but induced emf decreases, exponentially.}$

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
}