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Current Question (ID: 20400)

Question:

$\text{A moving coil galvanometer with a resistance of } 50 \, \Omega \text{ shows full deflection at a current of } 4 \, \text{mA.}$ $\text{When this galvanometer is used to construct a voltmeter with a series resistance of } 5 \, \text{k}\Omega, \text{ the maximum voltage that can be measured by the voltmeter is close to:}$

Options:

1. $40 \, \text{V}$
2. $10 \, \text{V}$
3. $15 \, \text{V}$
4. $20 \, \text{V}$

Solution:

$\text{Hint: } V = I_g(G + S)$ $\text{Step: Find the maximum voltage measured by the voltmeter.}$ $\text{Given: } G = 50 \, \Omega, \ I_g = 4 \, \text{mA}, \ S = 5 \, \text{k}\Omega$ $\text{The maximum voltage measured by the voltmeter is given by:}$ $V = I_g(G + S)$ $\Rightarrow V = 4 \times 10^{-3}(50 + 5000)$ $\Rightarrow V = 4 \times 10^{-3}(5050)$ $\Rightarrow V = 20200 \times 10^{-3} \approx 20 \, \text{V}$ $\text{Hence, option (4) is the correct answer.}$

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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
}