Import Question JSON

Current Question (ID: 20256)

Question:

$\text{A uniform wire of resistance } R \text{ is folded into a regular polygon of } n \text{ sides. The equivalent resistance of this system between any two adjacent points is:}$

Options:

1. $\frac{n-1}{n} R$
2. $\frac{n-1}{n^2} R$
3. $\frac{n-1}{n^3} R$
4. $\frac{n+1}{n^2} R$

Solution:

$\text{Hint: Recall the combination of series and parallel configuration.}$ $\text{Step 1: Draw the equivalent circuit diagram.}$ $\frac{R}{n} (n-1)$ $\frac{R}{n}$ $\text{Step 2: Find the equivalent resistance.}$ $R_{\text{eq}} = \frac{\frac{R}{n} (n-1) \times \frac{R}{n}}{\frac{R}{n} (n-1) + \frac{R}{n}}$ $= \frac{(n-1) \frac{R}{n}}{n} = \frac{n-1}{n^2} R$ $\text{Option (2) is correct.}$

Import JSON File

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
}