Import Question JSON

Current Question (ID: 16552)

Question:

$\text{The equivalent capacitance across } A \text{ and } B \text{ in the given figure is:}$

Options:

1. $\frac{3}{2}C$
2. $C$
3. $\frac{2}{3}C$
4. $\frac{5}{3}C$

Solution:

$\text{Hint: Rearrange the capacitors according to the potentials of their terminals.}$ $\text{Step 1: Find the equivalent capacitance of the capacitors in series.}$ $\text{The equivalent circuit diagram of the circuit is shown in the figure below;}$ $C' = \frac{C \times 2C}{C + 2C} = \frac{2C}{3}$ $\text{Step 2: The equivalent capacitance across } A \text{ and } B.\text{ The equivalent capacitance across } A \text{ and } B \text{ is given by;}$ $C_{AB} = \frac{2C}{3} + C = \frac{5C}{3}$ $\text{Hence, option (4) is the correct answer.}$

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
}