Import Question JSON

Current Question (ID: 17343)

Question:

$\text{One 10 V, 60 W bulb is to be connected to 100 V line. The required induction coil has a self-inductance of value:}$ $\left(f = 50 \text{ Hz}\right)$

Options:

1. $0.052 \text{ H}$
2. $2.42 \text{ H}$
3. $16.2 \text{ mH}$
4. $1.62 \text{ mH}$

Solution:

$\text{(1) Current through the bulb } i = \frac{P}{V} = \frac{60}{10} = 6 \text{ A}$ $V = \sqrt{V_R^2 + V_L^2}$ $(100)^2 = (10)^2 + V_L^2 \Rightarrow V_L = 99.5 \text{ Volt}$ $\text{Also } V_L = i X_L = i \times (2 \pi \nu L)$ $\Rightarrow 99.5 = 6 \times 2 \times 3.14 \times 50 \times L$ $\Rightarrow L = 0.052 \text{ H}$

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
}