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Current Question (ID: 16606)

Question:

$\text{The current in a wire varies with time according to the equation } I = (4 + 2t), \text{ where } I \text{ is in ampere and } t \text{ is in seconds. The quantity of charge which has passed through a cross-section of the wire during the time } t = 2 \text{ s to } t = 6 \text{ s will be:}$

Options:

1. $60 \text{ C}$
2. $24 \text{ C}$
3. $48 \text{ C}$
4. $30 \text{ C}$

Solution:

$\text{Hint: Use, } i = \frac{dq}{dt}. $ $\text{Step 1: Find the charge flowing in time } dt. $ $\text{Given, } i = 4 + 2t $ $\text{As, } i = \frac{dq}{dt} = (4 + 2t) $ $dq = (4 + 2t) dt $ $\text{Step 2: Integrate on both sides to calculate } (q_1 - q_2). $ $\int_{q_1}^{q_2} dq = \int_{2}^{6} (4 + 2t) \ dt $ $[q]_{q_1}^{q_2} = [4t + t^2]_{2}^{6} $ $(q_1 - q_2) = 48 \text{ C}$

Import JSON File

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
}