Import Question JSON

Current Question (ID: 20231)

Question:

$\text{Five equal resistances are connected in a network as shown in the figure. The net resistance between point } A \text{ and point } B \text{ is:}$

Options:

1. $\frac{2R}{R}$
2. $\frac{2}{3R}$
3. $\frac{3R}{2}$
4. $R$

Solution:

$\text{Hint: Identify the Wheatstone Bridge in the given circuit.}$ $\text{Step: Find the net resistance between points } A \text{ and } B. \text{ The equivalent circuit diagrams are shown in the figure below;} \text{The above circuit diagram is a balanced Wheatstone Bridge so the equivalent resistance between points } A \text{ and } B \text{ is given by;} R_{eq} = \frac{2R \times 2R}{2R + 2R} = R \text{Therefore, the net resistance between points } A \text{ and } B \text{ is } R. \text{Hence, option (4) is the correct answer.}$

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
}