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Current Question (ID: 20578)

Question:

$\text{In a series } LCR \text{ circuit, the inductance, capacitance and resistance are } L = 100 \text{ mH}, C = 100 \ \mu\text{F} \text{ and } R = 10 \, \Omega \text{ respectively.}$ $\text{They are connected to an AC source of voltage } 220 \, \text{V} \text{ and frequency of } 50 \, \text{Hz}. \text{ The approximate value of current in the circuit will be:}$

Options:

1. $15 \, \text{A}$
2. $32 \, \text{A}$
3. $22 \, \text{A}$
4. $14 \, \text{A}$

Solution:

$\text{Hint: } I = \frac{V}{Z}$

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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
}