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Current Question (ID: 20233)

Question:

$\text{Two identical cells, each of EMF } 1.5 \text{ V and internal resistance } r, \text{ are connected in parallel and used to supply a parallel combination of two resistors, each of resistance } 20 \, \Omega. \text{ A voltmeter across the resistor network reads } 1.2 \, \text{V. What is the internal resistance } r \text{ of each cell?}$

Options:

1. $2.5 \, \Omega$
2. $4 \, \Omega$
3. $5 \, \Omega$
4. $10 \, \Omega$

Solution:

$\text{Hint: } V = \varepsilon - Ir$ $\text{Step 1: Draw the circuit diagram.}$ $\text{Step 2: Find the value of current } I.$ $1.2 = I \times 10 \quad [\because V = IR]$ $\Rightarrow I = 0.12 \, \text{A}$ $\text{Step 3: Find the internal resistance of the cell.}$ $0.3 = I \times \frac{r}{2}$ $\Rightarrow 0.3 = 0.12 \times \frac{r}{2}$ $\Rightarrow r = 5 \, \Omega$ $\text{Hence, option (3) is the correct answer.}$

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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
}