Import Question JSON

Current Question (ID: 20204)

Question:

$\text{In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance } C \text{ will be:}$

Options:

1. $CE$
2. $CE \frac{r_1}{r_2 + r}$
3. $CE \frac{r_2}{r + r_2}$
4. $CE \frac{r_1}{r_1 + r}$

Solution:

$\text{Hint: At steady state current through capacitor branch become zero.}$ $i = \frac{E}{r + r_2}$ $\text{Potential difference across capacitor } \Delta V$ $\Delta V = i r_2$ $\Delta V = \left( \frac{E}{r + r_2} \right) r_2$ $\text{charge on capacitor} = C \Delta V$ $= CE \left( \frac{r_2}{r + r_2} \right)$

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
}