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Current Question (ID: 16850)

Question:

$\text{The galvanometer of resistance } 80 \, \Omega \text{ deflects a full scale for a potential of } 20 \, \text{mV.}$ $\text{How much resistance is required for a voltmeter to deflect a full scale of } 5 \, \text{V to be made using this galvanometer?}$

Options:

1. $\text{resistance of } 19.92 \, \text{k} \Omega \text{ parallel to the galvanometer}$
2. $\text{resistance of } 19.92 \, \text{k} \Omega \text{ in series with the galvanometer}$
3. $\text{resistance of } 20 \, \Omega \text{ parallel to the galvanometer}$
4. $\text{resistance of } 20 \, \Omega \text{ in series with the galvanometer}$

Solution:

$\text{Hint: External resistance must be connected in series.}$ $\text{Step 1: Find the current rating of the galvanometer}$ $i_g \, R_G = V$ $i_g = \frac{20 \times 10^{-3}}{80}$ $= 0.25 \, \text{mA}$ $\text{Step 2: Connect external resistance in series with galvanometers}$ $\text{Step 3: Find the external resistance}$ $5 = (80 + R) \, i_g$ $R + 80 = \frac{5}{0.25 \times 10^{-3}}$ $R + 80 = 20 \, \text{k} \Omega$ $R = 19.92 \, \text{k} \Omega$

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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
}