Import Question JSON

Current Question (ID: 20451)

Question:

$\text{Consider the circuit shown. The galvanometer resistance is } 10 \, \Omega \text{ and current through the galvanometer is } 3 \, \text{mA.}$ $\text{Then the resistance of the shunt is:}$

Options:

1. $10^{-3} \, \Omega$
2. $7.5 \times 10^{-3} \, \Omega$
3. $6.75 \times 10^{-3} \, \Omega$
4. $3.75 \times 10^{-3} \, \Omega$

Solution:

$\text{Hint: } G \text{ and } S \text{ are in parallel then } V_G = V_S.$ $\text{Since } G \text{ and } S \text{ are in parallel}$ $\Rightarrow V_G = V_S$ $\Rightarrow 3 \, \text{mA} \times 10 = 8 \, \text{A} \times R_S$ $\Rightarrow R_S = 3.75 \, \text{m} \Omega$

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
}