Import Question JSON

Current Question (ID: 20602)

Question:

$\text{The alternating voltage and current in a circuit are given by:}$ $V = 100 \sin(\omega t) \text{ volts and } I = 100 \sin\left(\omega t + \frac{\pi}{3}\right) \text{ milliamperes.}$ $\text{The average power dissipated in the circuit is:}$ $1.\ 2.5 \text{ W}$ $2.\ 5 \text{ W}$ $3.\ 10 \text{ W}$ $4.\ 20 \text{ W}$

Options:

1. $2.5 \text{ W}$
2. $5 \text{ W}$
3. $10 \text{ W}$
4. $20 \text{ W}$

Solution:

$\text{Hint: } P_{\text{avg}} = V_{\text{rms}} I_{\text{rms}} \cos \phi$ $\text{Step: Find the average power dissipated in the circuit.}$ $P_{\text{avg}} = V_{\text{rms}} I_{\text{rms}} \cos \phi$ $\Rightarrow P_{\text{avg}} = \frac{100}{\sqrt{2}} \times \frac{100 \times 10^{-3}}{\sqrt{2}} \cos 60^\circ$ $\Rightarrow P_{\text{avg}} = 2.5 \text{ W}$ $\text{Hence, option (1) is the correct answer.}$

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
}