Import Question JSON

Current Question (ID: 20337)

Question:

$\text{A galvanometer having a coil resistance of } 100 \, \Omega \text{ gives a full-scale deflection when a current of } 1 \, \text{mA} \text{ is passed through it. The value of the resistance which can convert this galvanometer into an ammeter giving a full-scale deflection for a current of } 10 \, \text{A} \text{, is:}$

Options:

1. $0.01 \, \Omega$
2. $2 \, \Omega$
3. $0.1 \, \Omega$
4. $3 \, \Omega$

Solution:

$\text{Hint: } s = \frac{i_g \times G}{i - i_g}$ $G = 100 \, \Omega$ $i_g = 1 \, \text{mA} = 10^{-3} \, \text{A}$ $i = 10 \, \text{A}$ $s = ?$ $s = \frac{i_g \times G}{i - i_g}$ $= \frac{10^{-3} \times 100}{10 - 10^{-3}}$ $= \frac{10^{-3} \times 100}{10}$ $= 10^{-2} \, \Omega$

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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
}