Import Question JSON

Current Question (ID: 20554)

Question:

$\text{In the AC circuit shown in the figure, the value of } I_{\text{rms}} \text{ is equal to:}$ $X_C = 100 \, \Omega$ $X_L = 100 \, \Omega$ $R = 100 \, \Omega$ $V = 200 \sqrt{2} \sin(\omega t)$

Options:

1. $2 \, \text{A}$
2. $2 \sqrt{2} \, \text{A}$
3. $4 \, \text{A}$
4. $\sqrt{2} \, \text{A}$

Solution:

$Z = \sqrt{R^2 + (X_L - X_C)^2}$ $Z = \sqrt{100^2 + (100 - 100)^2} = 100 \, \Omega$ $\text{So,}$ $i_0 = \frac{V_0}{Z} = \frac{200 \sqrt{2}}{100} = 2 \sqrt{2}$ $i_{\text{rms}} = \frac{i_0}{\sqrt{2}} = 2 \, \text{A}$

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
}