Import Question JSON

Current Question (ID: 16677)

Question:

$\text{A 50 kW dc generator produces a potential difference of 250 V. If the resistance of the transmission line is 1 } \Omega, \text{ what percentage of the original power is lost during transmission?}$ $1. \ 80\%$ $2. \ 40\%$ $3. \ 20\%$ $4. \ 10\%$

Options:

1. 80\%
2. 40\%
3. 20\%
4. 10\%

Solution:

$\text{Hint: Power loss = } I^2R$ $\text{Step 1: Find the current in the transmission line.}$ $P = VI_C$ $I_C = \frac{P}{V} = \frac{50 \times 10^3}{250} = 200 \text{ A}$ $\text{Step 2: Find the power loss in the transmission line.}$ $P_{\text{loss}} = I_C^2 R = (200)^2 = 40 \text{ kW}$ $\text{Step 3: Find the percentage loss in power in the transmission line.}$ $\% \text{ loss} = \frac{P_{\text{loss}}}{P_i} \times 100 = \frac{40}{50} \times 100 = 80\%$

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
}