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Current Question (ID: 17273)

Question:
$\text{The variation of EMF with time for four types of generators is shown in the figures. Which amongst them can be called AC voltage?}$
Options:
  • 1. $(a) \text{ and } (d)$
  • 2. $(a), (b), (c), \text{ and } (d)$
  • 3. $(a) \text{ and } (b)$
  • 4. $\text{only } (a)$
Solution:
$\text{Hint: AC voltage changes periodically with time.}$ $\text{Explanation: In AC voltage, the voltage varies in both magnitude and polarity with time. In all the cases, the voltage is changing with time periodically.}$ $\text{An alternating Current (AC) is defined as a current (or voltage) that periodically reverses its direction, meaning it alternates between positive and negative values over time.}$ $\text{The waveform of an AC voltage typically involves a sinusoidal shape, but it can also include other waveforms like triangular or square waves as long as they alternate between positive and negative values.}$ $\text{Figure (a): This is a sinusoidal waveform that alternates between positive and negative values. This is a standard AC voltage.}$ $\text{Figure (b): This is a square waveform that alternates between positive and negative values. Square waves can also represent AC voltage.}$ $\text{Figure (c): This waveform starts at zero, rises to a positive value, then drops back to zero, and repeats. Even though it is not continuously alternating between positive and negative values, it is still AC because it is periodically varying, and the voltage returns to zero before repeating. Hence, it can be considered AC voltage.}$ $\text{Figure (d): This is a triangular waveform that alternates between positive and negative values. This is another form of AC voltage.}$ $\text{All four waveforms represent alternating current (AC) in some form, even though their shapes differ.}$ $\text{Hence, option (2) is the correct answer.}$

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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
}