Import Question JSON

Current Question (ID: 20546)

Question:

$\text{Find the peak current and resonant frequency of the following circuit}$ $\text{(as shown in the figure).}$

Options:

1. $0.2 \text{ A and } 50 \text{ Hz}$
2. $0.2 \text{ A and } 100 \text{ Hz}$
3. $2 \text{ A and } 100 \text{ Hz}$
4. $2 \text{ A and } 50 \text{ Hz}$

Solution:

$\text{Hint: } f = \frac{1}{2\pi\sqrt{LC}}.$ $x_L = \omega L = 100 \times 100 \times 10^{-3} = 10\Omega$ $x_C = \frac{1}{\omega C} = \frac{1}{100 \times 100 \times 10^{-6}} = 10\Omega$ $z = \sqrt{(x_L - x_C)^2 + R^2} = \sqrt{90^2 + 120^2} = 150\Omega$ $i_{\text{peak}} = \frac{\Delta v}{z} = \frac{30}{150} = 0.2 \text{ amp}$ $\text{For resonant frequency: } \omega L = \frac{1}{\omega C} \Rightarrow \omega^2 = \frac{1}{LC} \Rightarrow \omega = \frac{1}{\sqrt{LC}}$ $f = \frac{1}{2\pi\sqrt{LC}} = \frac{100}{2\pi} = 50 \text{ Hz}$

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
}