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Current Question (ID: 16964)

Question:

$\text{Some magnetic flux is changed from a coil of resistance } 10 \, \Omega. \text{ As a result, an induced current is developed in it, which varies with time as shown in the figure. The magnitude of change in flux through the coil in Wb is:}$ $\begin{array}{c} i \, (\text{A}) \\ | \\ 4 \\ \end{array}$ $\begin{array}{c} \rightarrow \\ \end{array}$ $\begin{array}{c} 0.1 \, t \, (\text{s}) \\ \end{array}$

Options:

1. $2$
2. $4$
3. $6$
4. $\text{None of these}$

Solution:

$\text{The induced current } i = \frac{\Delta \Phi}{R \Delta t} \text{ where } \Delta \Phi \text{ is the change in flux, } R \text{ is resistance, and } \Delta t \text{ is the change in time.}$ $\text{From the graph, } i = 4 \, \text{A}, \Delta t = 0.1 \, \text{s}, \text{ and } R = 10 \, \Omega.$ $\Delta \Phi = i \times R \times \Delta t = 4 \times 10 \times 0.1 = 4 \, \text{Wb}$

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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
}