Import Question JSON

Current Question (ID: 17338)

Question:

$\text{An inductor } (L) \text{ and resistance } (R) \text{ are connected in series with an AC source.}$ $\text{The phase difference between voltage } (V) \text{ and current } (i) \text{ is } 45^\circ. \text{ If the phase difference between } V \text{ and } i \text{ remains the same, then the capacitive reactance and impedance of the } LCR \text{ circuit will be:}$

Options:

1. $2R, R\sqrt{2}$
2. $R, R\sqrt{2}$
3. $R, R$
4. $2R, R\sqrt{3}$

Solution:

$\tan 45^\circ = \frac{X_L}{R} \Rightarrow X_L = R$ $\tan 45^\circ = \frac{X_C - X_L}{R} \Rightarrow R = X_C - R \Rightarrow X_C = 2R$ $Z = \sqrt{R^2 + (X_C - X_L)^2} = R\sqrt{2}$

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
}