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Current Question (ID: 20547)

Question:

$\text{Given below are two statements:}$ $\text{Statement I: The reactance of an AC circuit is zero. It is possible that the circuit contains a capacitor and an inductor.}$ $\text{Statement II: In an AC circuit, the average power delivered by the source never becomes zero.}$

Options:

1. $\text{Both Statement I and Statement II are True.}$
2. $\text{Both Statement I and Statement II are False.}$
3. $\text{Statement I is True but Statement II is False.}$
4. $\text{Statement I is False but Statement II is True.}$

Solution:

$\text{Hint: If } R = 0 \text{ the average power delivered by the source becomes zero.}$ $\text{Explanation: In a circuit, reactance can be zero either if there are no inductors and capacitors in the circuit, or if the individual reactance of inductors and capacitors cancel each other, making net reactance zero.}$ $\text{In an AC circuit, the average power the source delivers becomes zero when the circuit contains only inductance or capacitance, or a combination of inductance and capacitance. The resistance should be zero.}$

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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
}