Import Question JSON

Current Question (ID: 16597)

Question:

$100$ capacitors each having a capacity of $10 \, \mu \text{F}$ are connected in parallel and are charged by a potential difference of $100 \, \text{kV}$. The energy stored in the capacitors and the cost of charging them, if electrical energy costs $108$ paise per kWh, will be?

Options:

1. $10^7 \text{ joule and } 300 \text{ paise}$
2. $5 \times 10^6 \text{ joule and } 300 \text{ paise}$
3. $5 \times 10^6 \text{ joule and } 150 \text{ paise}$
4. $10^7 \text{ joule and } 150 \text{ paise}$

Solution:

$\text{Energy stored in the capacitor} = \frac{1}{2} CV^2 \times 100$ $= \frac{1}{2} \times 10 \times 10^{-6} \times (100 \times 10^3)^2 \times 100 = 5 \times 10^6 \text{ J}$ $1 \text{ kWh} = 1 \times 10^3 \times 60 \times 60 \text{ J} = 3.6 \times 10^6 \text{ J}$ $\text{As price of } 3.6 \times 10^6 \text{ J energy} = 108 \text{ Paise per kWh}$ $\text{So, price of 1 J energy} = \frac{108}{3.6 \times 10^6} \text{ Paisa}$ $\therefore \text{Total cost of charging} = \frac{5 \times 10^6 \times 108}{3.6 \times 10^6} = 150 \text{ Paise}$

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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
}