Import Question JSON

Current Question (ID: 17334)

Question:

$\text{A constant voltage at different frequencies is applied across a capacitance } C$ $\text{as shown in the figure.}$ $\text{Which of the following graphs accurately illustrates how current varies with frequency?}$

Options:

1. $\text{Graph 1: Increasing curve of } I \text{ vs. } \omega$
2. $\text{Graph 2: Linear increase of } I \text{ vs. } \omega$
3. $\text{Graph 3: Decreasing curve of } I \text{ vs. } \omega$
4. $\text{Graph 4: Constant } I \text{ vs. } \omega$

Solution:

$\text{For capacitive circuits } X_C = \frac{1}{\omega C}$ $\therefore \ I = \frac{V}{X_C} = V \omega C \Rightarrow I \propto \omega$

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
}