Import Question JSON

Current Question (ID: 17361)

Question:

$\text{How much power is dissipated in an } LCR \text{ series circuit connected to an } AC \text{ source of emf } E?$

Options:

1. $\frac{\varepsilon^2 R}{R^2 + \left( L\omega - \frac{1}{C\omega} \right)^2}$
2. $\frac{\varepsilon^2 \sqrt{R^2 + \left( L\omega - \frac{1}{C\omega} \right)^2}}{R}$
3. $\frac{\varepsilon^2 \left[ R^2 + \left( L\omega - \frac{1}{C\omega} \right)^2 \right]}{R}$
4. $\frac{\varepsilon^2 R}{\sqrt{R^2 + \left( L\omega - \frac{1}{C\omega} \right)^2}}$

Solution:

$E_0 = \sqrt{V^2_R + (V_L - V_C)^2}$ $E_0 = I_0 \sqrt{R^2 + (X_L - X_C)^2}$ $X_L = L\omega$ $X_C = \frac{1}{C\omega}$ $\frac{E_0}{I_0} = \sqrt{R^2 + \left( L\omega - \frac{1}{C\omega} \right)^2}$ $P = I^2_{\text{rms}} R = \frac{\varepsilon^2_{\text{rms}} R}{|Z|^2} = \frac{\varepsilon^2 R}{R^2 + \left( \omega L - \frac{1}{\omega C} \right)^2}$

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
}