Import Question JSON

Current Question (ID: 20590)

Question:

$\text{The equation of current in a purely inductive circuit is}$ $5 \sin(49 \pi t - 30^\circ).$ $\text{If the inductance is 30 mH, then the equation for the voltage across the inductor will be:}$ $\left( \text{Let } \pi = \frac{22}{7} \right)$

Options:

1. $1.47 \sin(49 \pi t - 30^\circ)$
2. $1.47 \sin(49 \pi t - 60^\circ)$
3. $23.1 \sin(49 \pi t - 30^\circ)$
4. $23.1 \sin(49 \pi t - 60^\circ)$

Solution:

$X_L = \omega L$ $X_L = 49 \pi \times 30 \times 10^{-3}$ $= 4.62$ $V = I X_L = 5 \times 4.62 = 23.1$ $\text{Phase difference is } 90^\circ$ $\text{Voltage leads current by } 90^\circ$ $\text{So, } V = 23.1 \sin(49 \pi t - 60^\circ)$

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
}