Import Question JSON

Current Question (ID: 17390)

Question:
$\text{A variable frequency AC source is connected to a capacitor. Then on increasing the frequency:}$
Options:
  • 1. $\text{Both conduction current and displacement current will increase}$
  • 2. $\text{Both conduction current and displacement current will decrease}$
  • 3. $\text{Conduction current will increase and displacement current will decrease}$
  • 4. $\text{Conduction current will decrease and displacement current will increase}$
Solution:
$\text{As the frequency increases, both the conduction current and displacement current increase due to the decreasing capacitive reactance and higher rate of change of the electric field.}$ $\text{When the frequency of the AC source increases:}$ $\text{Conduction current increases because the capacitive reactance decreases with higher frequency, allowing more current to flow. The conduction current } I \text{ in a capacitor is related to the voltage } V \text{ and the capacitive reactance } X_C \text{ by:}$ $I = \frac{V}{X_C} \text{ As the frequency increases, } X_C \text{ decreases, so the conduction current increases.}$ $\text{Displacement current increases because the rate of change of the electric field across the capacitor increases with frequency. The displacement current in a capacitor is related to the rate of change of the electric field across the capacitor, which depends on the frequency of the AC source. A higher frequency causes a greater rate of change of the electric field, which increases the displacement current. Therefore, both the conduction current and displacement current increase as the frequency increases. Hence, option (1) is the correct answer.}$

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
}