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Current Question (ID: 17022)

Question:

$\text{A pair of adjacent coils has a mutual inductance of } 1.5 \text{ H. If the current in one coil changes from } 0 \text{ to } 20 \text{ A in } 0.5 \text{ s, what is the change of flux linkage with the other coil?}$

Options:

1. $35 \text{ Wb}$
2. $25 \text{ Wb}$
3. $30 \text{ Wb}$
4. $20 \text{ Wb}$

Solution:

$\text{Hint: } \phi = M \times I$ $\text{Step: Find the flux through the second coil due to the current in the first coil.}$ $\text{The change in flux linkage with the second coil can be found using the relation for mutual inductance given by:}$ $\Delta \phi = M \times \Delta I$ $\Delta \phi_{21} = M \Delta i_1$ $\text{Substituting the known values we get,}$ $\Delta \phi_{21} = 1.5 \times 20$ $\Rightarrow \Delta \phi_{21} = 30 \text{ Wb}$ $\text{Hence, option (3) is the correct answer.}$

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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
}