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Current Question (ID: 20518)

Question:

$\text{The magnetic flux through a coil perpendicular to its plane is varying according to the relation } \phi = (5t^3 + 4t^2 + 2t - 5) \text{ Wb. If the resistance of the coil is } 5 \, \Omega, \text{ then the induced current through the coil at } t = 2 \, \text{s will be:}$ $1. \, 15.6 \, \text{A}$ $2. \, 16.6 \, \text{A}$ $3. \, 17.6 \, \text{A}$ $4. \, 18.6 \, \text{A}$

Options:

1. $15.6 \, \text{A}$
2. $16.6 \, \text{A}$
3. $17.6 \, \text{A}$
4. $18.6 \, \text{A}$

Solution:

$\text{Hint: } \varepsilon = \frac{d\phi}{dt}$ $\text{Step: Find the current induced in the coil.}$ $\text{The induced current is given by:}$ $\Rightarrow \, i = \frac{\varepsilon}{R} = \frac{1}{R} \left| \frac{d\phi}{dt} \right|$ $\text{Substitute the given values we get;}$ $\Rightarrow \, i = \frac{1}{5} (15t^2 + 8t + 2)$ $\text{at } t = 2 \, \text{s we get;}$ $\Rightarrow \, i = \frac{1}{5} (15 \times 4 + 8 \times 2 + 2) = 15.6 \, \text{A}$ $\text{Hence, option (1) is the correct answer.}$

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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
}