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Current Question (ID: 17339)

Question:

$\text{In a series } LCR \text{ circuit, which one of the following curves represents the variation of impedance } (Z) \text{ with frequency } (f)?$

Options:

1. $\text{Option 1: Decreasing curve}$
2. $\text{Option 2: Bell-shaped curve}$
3. $\text{Option 3: U-shaped curve}$
4. $\text{Option 4: Linear increasing curve}$

Solution:

$Z = \sqrt{R^2 + \left(2\pi f L - \frac{1}{2\pi f C}\right)^2}$ $\text{From above equation at } f = 0 \Rightarrow z = \infty$ $\text{When } f = \frac{1}{2\pi \sqrt{LC}} \text{ (resonant frequency)}$ $Z = R \text{ which is the minimum value}$

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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
}