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Current Question (ID: 20563)

Question:

$\text{A sinusoidal voltage of peak value } 283 \text{ V and angular frequency } 320 \text{ s}^{-1} \text{ is applied to a series LCR circuit. Given that } R = 5 \, \Omega, \, L = 25 \, \text{mH and } C = 1000 \, \mu\text{F. The total impedance, and phase difference between the voltage across the source and the current will respectively be:}$

Options:

1. $10 \, \Omega \text{ and } \tan^{-1}\left(\frac{5}{3}\right)$
2. $10 \, \Omega \text{ and } \tan^{-1}\left(\frac{8}{3}\right)$
3. $7 \, \Omega \text{ and } \tan^{-1}\left(\frac{5}{3}\right)$
4. $7 \, \Omega \text{ and } 45^\circ$

Solution:

$\text{Hint: } \tan \phi = \frac{X_L - X_C}{R}$ $X_C = \frac{1}{\omega C}$

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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
}