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Current Question (ID: 16681)

Question:

$\text{A voltmeter of resistance } 660 \, \Omega \text{ reads the voltage of a very old cell to be } 1.32 \, \text{V while a potentiometer reads its voltage to be } 1.44 \, \text{V. The internal resistance of the cell is:}$

Options:

1. $30 \, \Omega$
2. $60 \, \Omega$
3. $6 \, \Omega$
4. $0.6 \, \Omega$

Solution:

$\text{Hint: The relation between emf and internal resistance is given as,}$ $V = E - Ir$ $\text{Step 1: Draw the circuit diagram for the voltmeter.}$ $\text{Step 2: Find the current through the voltmeter.}$ $\text{The emf of the cell is } E = 1.44 \, \text{V}$ $R_V = 660 \, \Omega$ $i = \frac{E}{R_V + r}$ $\text{Step 3: Find the internal resistance of the cell.}$ $V = E - ir$ $1.32 = E - \frac{Er}{R + r}$ $\Rightarrow 1.32 = \frac{E(R + r) - Er}{R + r} = \frac{1.44 \, R}{R + r}$ $r = \frac{R}{11} = 60 \, \Omega$ $\text{Hence, option (2) is the correct answer.}$

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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
}