Import Question JSON

Current Question (ID: 20496)

Question:

$\text{Two concentric circular coils, } C_1 \text{ and } C_2, \text{ are placed in the } XY \text{ plane.}$ $C_1 \text{ has } 500 \text{ turns, and a radius of } 1 \text{ cm.}$ $C_2 \text{ has } 200 \text{ turns and radius of } 20 \text{ cm.}$ $C_2 \text{ carries a time dependent current } I(t) = (5t^2 - 2t + 3) \text{ A where } t \text{ is in } s.$ $\text{The emf induced in } C_1 \text{ (in mV), at the instant } t = 1 \text{ s is } \frac{4}{x}. \text{ The value of } x \text{ is:}$

Options:

1. 1
2. 5
3. 7
4. 9

Solution:

$\text{Hint: } \varepsilon = \frac{d\phi}{dt}$ $B = \frac{\mu_0 NI}{2R}$ $\phi = \frac{\mu_0 NN'I}{2R} \pi r^2$ $\varepsilon = \frac{d\phi}{dt} = \frac{2\pi \times 10^{-7} \times 10^5 \times \pi \times 10^4}{0.2}$ $= 8 \times 10^{-4} = 0.8 \text{ mV}$

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
}