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Current Question (ID: 17282)

Question:

$\text{When an alternating voltage is given as;} \ E = (6 \sin \omega t - 2 \cos \omega t) \ \text{V}, \ \text{what is its RMS value?}$

Options:

1. $4\sqrt{2} \ \text{V}$
2. $2\sqrt{5} \ \text{V}$
3. $2\sqrt{3} \ \text{V}$
4. $4 \ \text{V}$

Solution:

$\text{Hint:} \ E_{\text{rms}} = \frac{E_0}{\sqrt{2}}$ $\text{Step: Find the RMS value of an alternating voltage.}$ $\text{Given;} \ E = (6 \sin \omega t - 2 \cos \omega t) \ \text{V},$ $E_0 = \sqrt{6^2 + 2^2}$ $E_0 = \sqrt{40} = 2\sqrt{10}$ $E_{\text{rms}} = \frac{E_0}{\sqrt{2}} = \frac{2\sqrt{10}}{\sqrt{2}}$ $= \frac{2 \times \sqrt{5} \times \sqrt{2}}{\sqrt{2}}$ $\Rightarrow E_{\text{rms}} = 2\sqrt{5} \ \text{V}$ $\text{Hence, option (2) is the correct answer.}$

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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
}