Import Question JSON

Current Question (ID: 20568)

Question:

$\text{A transformer consisting of } 300 \text{ turns in the primary and } 150 \text{ turns in the secondary gives output power of } 2.2 \text{ kW.}$ $\text{If the current in the secondary coil is } 10 \text{ A, then the input voltage and current in the primary coil are:}$

Options:

1. $440 \text{ V and } 20 \text{ A}$
2. $440 \text{ V and } 5 \text{ A}$
3. $220 \text{ V and } 20 \text{ A}$
4. $220 \text{ V and } 10 \text{ A}$

Solution:

$\text{Hint: } \frac{i_s}{i_p} = \frac{n_p}{n_s}$ $n_p = 300, \ n_s = 150$ $\frac{i_s}{i_p} = \frac{n_p}{n_s}$ $i_p = \frac{i_s \ n_s}{n_p} = 5 \text{ A}$ $P_s = V_s i_s = V_s = \frac{2.2 \times 10^3}{10} = 220$ $V_p = V_s \frac{n_p}{n_s} = 220 \times \frac{300}{150} = 440 \text{ V}$

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
}