Import Question JSON

Current Question (ID: 16551)

Question:

$\text{Three capacitors each of capacitance } C \text{ and of breakdown voltage } V \text{ are joined in series. The capacitance and breakdown voltage of the combination will be:}$

Options:

1. $\frac{C}{3}, \frac{V}{3}$
2. $3C, \frac{V}{3}$
3. $\frac{C}{3}, 3V$
4. $3C, 3V$

Solution:

$\text{In series arrangement charge on each plate of each capacitor has the same magnitude.}$ $\text{The potential difference is distributed inversely in the ratio of capacitors i.e,}$ $V = V_1 + V_2 + V_3 \ldots$ $\text{Here, the net potential drop across the capacitors, } V' = 3V$ $\text{The equivalent capacitance } C_s \text{ is given by:}$ $\frac{1}{C_s} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \ldots$ $C_s = \frac{C}{3}$

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
}