Import Question JSON

Current Question (ID: 17355)

Question:

$\text{The potential differences across the resistance, capacitance and inductance are } 80 \text{ V, } 40 \text{ V and } 100 \text{ V respectively in an } LCR \text{ circuit. What is the power factor of this circuit?}$ $1.\ 0.4$ $2.\ 0.5$ $3.\ 0.8$ $4.\ 1.0$

Options:

1. $0.4$
2. $0.5$
3. $0.8$
4. $1.0$

Solution:

$\text{Power factor of the L-C-R circuit}$ $= \cos \phi = \frac{R}{Z}$ $= \frac{IR}{IZ} = \frac{IR}{\sqrt{(IX_L - IX_C)^2 + (IR)^2}}$ $= \frac{80}{\sqrt{(100 - 40)^2 + (80)^2}}$ $= \frac{80}{\sqrt{(60)^2 + (80)^2}} = \frac{80}{100} = 0.8$

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
}