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Current Question (ID: 17291)

Question:

$\text{An alternating voltage (in volts) given by } V = 200\sqrt{2} \sin 100t \text{ is connected to a } 1 \, \mu F \text{ capacitor through an AC ammeter. The reading of the ammeter will be:}$

Options:

1. $10 \, \text{mA}$
2. $20 \, \text{mA}$
3. $40 \, \text{mA}$
4. $80 \, \text{mA}$

Solution:

$V = 200\sqrt{2} \sin(100t)$ $V_0 = 200\sqrt{2} \, \text{V}$ $\omega = 100 \, \text{rad/s}$ $V_{\text{rms}} = \frac{V_0}{\sqrt{2}} = \frac{200\sqrt{2}}{\sqrt{2}} = 200 \, \text{V}$ $\text{Now, } X_C = \frac{1}{\omega C} = \frac{1}{100 \times 1 \times 10^{-6}} = 10^4 \, \Omega$ $\text{Reading of the ammeter, } I_{\text{rms}} = \frac{V_{\text{rms}}}{X_C} = \frac{200}{10^4} = 20 \times 10^{-3} \, \text{A}$ $= 20 \, \text{mA}$

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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
}