Import Question JSON

Current Question (ID: 20220)

Question:

$\text{An ideal cell of emf } 10 \text{ V is connected in circuit shown in figure. Each resistance is } 2 \, \Omega. \text{ The potential difference (in V) across the capacitor when it is fully charged is:}$

Options:

1. $2$
2. $4$
3. $6$
4. $8$

Solution:

$\text{Potential difference across the capacitor} = V_{R_2} + V_{R_1}$ $R_1 \text{ to } R_5 \rightarrow \text{ each } 2 \, \Omega$ $\text{Cap. is fully charged}$ $\text{So no current is there in branch ADB}$ $\text{Effective circuit of current flow:}$ $R_{eq} = \left( \frac{4 \times 2}{4 + 2} \right) + 2$ $R_{eq} = \frac{4}{3} + 2 = \frac{10}{3} \, \Omega$ $i = \frac{10}{10/3} = 3 \, \text{A}$ $\text{So potential different across AEB}$ $\Rightarrow 2 \times 1 + 2 \times 3 = 8 \, \text{V}$ $\text{Hence potential difference across}$ $\text{Capacitor} = \Delta V = V_{AEB} = 8 \, \text{V}$

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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
}