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Current Question (ID: 20549)

Question:

$\text{An AC source is connected to an inductance of } 100 \text{ mH, a capacitance of } 100 \ \mu\text{F and resistance of } 120 \ \Omega \text{ as shown in the figure.}$ $\text{The time in which the resistance having a thermal capacity of } 2 \ \text{J/}^\circ\text{C will get heated by } 16^\circ\text{C is:}$

Options:

1. $15 \ \text{s}$
2. $20 \ \text{s}$
3. $25 \ \text{s}$
4. $30 \ \text{s}$

Solution:

$\text{Hint: } i_{\text{rms}} = \frac{V_{\text{rms}}}{Z}$ $| (X_L - X_C) | = | 10 - 10^2 | = 90 \ \Omega$ $Z = \text{Impedance}$ $= \sqrt{(X_L - X_C)^2 + R^2} = \sqrt{(90)^2 + (20)^2} = 150 \ \Omega$ $i_{\text{rms}} = \frac{V_{\text{rms}}}{z} = \left( \frac{2}{15} \right) \text{ A}$ $\text{Now } i_{\text{rms}}^2 R \Delta t = ms(\Delta T)$ $\Rightarrow \Delta t = 15 \text{ sec}$

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
}