Import Question JSON

Current Question (ID: 20500)

Question:

$\text{The current } (i) \text{ at time } t = 0 \text{ and } t = \infty \text{ respectively for the given circuit is:}$

Options:

1. $\frac{18E}{55}, \frac{5E}{10}$
2. $\frac{33}{5E}, \frac{18E}{5}$
3. $\frac{33}{5E}, 18$
4. $\frac{18}{5E}, \frac{55}{10E}$

Solution:

$\text{Hint: After a long time, the inductor acts as a conducting wire.}$ $\text{At } t = 0, \text{ current through inductor is zero,}$ $\text{hence } R_{\text{eq}} = \left(5 + 1\right) \parallel \left(5 + 4\right) = \frac{18}{5}$ $i_1 = \frac{E}{18/5} = \frac{5E}{18}$ $\text{At } t = \infty, \text{ inductor becomes a simple wire and now the circuit will be as shown in figure}$ $\text{hence } R_{\text{eq}} = \left(5 \parallel 5\right) + \left(4 \parallel 1\right) = \frac{33}{10}; \left(\parallel \Rightarrow \text{ parallel}\right)$ $i_2 = \frac{E}{33/10} = \frac{10E}{33}$

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
}