Import Question JSON

Current Question (ID: 16637)

Question:

$\text{The effective resistance between points } P \text{ and } Q \text{ of the electrical circuit shown in the figure is:}$

Options:

1. $\frac{2Rr}{(R+r)}$
2. $\frac{8R(R+r)}{(3R+r)}$
3. $2r + 4R$
4. $\frac{5R}{2} + 2r$

Solution:

$\text{In a circuit, any circuit element placed between points at the same potential can be removed, without affecting the rest of the circuit.}$ $\text{Here, by symmetry, points } A, B \text{ and } C \text{ are at the same potential, for any potential difference between } P \text{ and } Q.$ $\text{The circuit can therefore be reduced as shown below:}$ $\text{Effective resistance } R_{eq} = \frac{2Rr}{R+r}.$

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
}