Import Question JSON

Current Question (ID: 16714)

Question:

$\text{In the following circuit, the battery } E_1 \text{ has an emf of } 12 \text{ volts and zero internal resistance while the battery } E \text{ has an emf of } 2 \text{ volts.}$ $\text{If the galvanometer } G \text{ reads zero, then the value of the resistance } X \text{ in ohms is:}$

Options:

1. $10$
2. $100$
3. $500$
4. $200$

Solution:

$\text{Since the galvanometer reads zero, the potential difference across } X \text{ is equal to the potential difference across the } 500 \Omega \text{ resistor.}$ $\text{Thus, } \frac{E_1}{500} = \frac{E}{X} \Rightarrow \frac{12}{500} = \frac{2}{X} \Rightarrow X = 100 \Omega$

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
}