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Current Question (ID: 17352)

Question:

$\text{A coil of inductive reactance of } 31 \, \Omega \text{ has a resistance of } 8 \, \Omega. \text{ It is placed in series with a condenser of capacitive reactance } 25 \, \Omega. \text{ The combination is connected to an AC source of } 110 \, \text{V. The power factor of the circuit is:}$

Options:

1. $0.56$
2. $0.64$
3. $0.80$
4. $0.33$

Solution:

$\text{Power factor of a.c. circuit is given by:}$ $\cos \phi = \frac{R}{Z}$ $\text{Given } R = 8 \, \Omega, \; X_L = 31 \, \Omega, \; X_C = 25 \, \Omega$ $\therefore \cos \phi = \frac{8}{\sqrt{8^2 + (31 - 25)^2}}$ $= \frac{8}{\sqrt{64 + 36}}$ $= \frac{8}{10}$ $\text{Hence, } \cos \phi = 0.80$

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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
}