Import Question JSON

Current Question (ID: 20338)

Question:

$\text{When a current of } 5 \text{ mA is passed through a galvanometer having a coil of resistance } 15 \, \Omega, \text{ it shows full scale deflection.}$ $\text{The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range } 0-10 \, \text{V is:}$

Options:

1. $1.985 \times 10^3 \, \Omega$
2. $2.045 \times 10^3 \, \Omega$
3. $2.535 \times 10^3 \, \Omega$
4. $4.005 \times 10^3 \, \Omega$

Solution:

$\text{Hint: } \Delta V_{\text{max}} = I_{g \text{max}} \left( R_g + R_H \right)$ $I_{g \text{max}} = 5 \, \text{mA} , \, R_g = 15 \, \Omega$ $\text{Range of voltmeter} = 10 \, \text{volt}$ $\Delta V = I_g \left( R_g + R_H \right)$ $\text{Range } \Delta V_{\text{max}} = I_{g \text{max}} \left( R_g + R_H \right)$ $10 = 5 \times 10^{-3} \left( 15 + R_H \right)$ $R_H = 1985 \, \Omega$ $R_H = 1.985 \times 10^3 \, \Omega$

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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
}