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Current Question (ID: 20594)

Question:

$\text{A capacitor of capacitance } 500 \, \mu\text{F is charged completely using a dc supply of } 100 \, \text{V. It is now connected to an inductor of inductance } 50 \, \text{mH to form an } LC \text{ circuit. The maximum current in the } LC \text{ circuit will be:}$ $1. \; 10 \, \text{A}$ $2. \; 20 \, \text{A}$ $3. \; 30 \, \text{A}$ $4. \; 40 \, \text{A}$

Options:

1. $10 \, \text{A}$
2. $20 \, \text{A}$
3. $30 \, \text{A}$
4. $40 \, \text{A}$

Solution:

$\text{Hint: Energy stored in capacitor=} \frac{1}{2} CV^2$ $\text{Step: Find the maximum current through the inductor.}$ $\text{When the complete energy is stored in the inductor, the current will be maximum.}$ $\frac{1}{2} CV^2_{\text{max}} = \frac{1}{2} LI^2_{\text{max}}$ $I_{\text{max}} = \sqrt{\frac{CV^2_{\text{max}}}{L}} = \sqrt{\frac{500 \times 10^{-6} \times 100^2}{50 \times 10^{-3}}} = 10 \, \text{A}$

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
}