Import Question JSON

Current Question (ID: 17015)

Question:

$\text{A coil of self-inductance } L \text{ is connected in series with a bulb } B \text{ and an AC source.}$ $\text{The brightness of the bulb decreases when:}$

Options:

1. $\text{number of turns in the coil is reduced.}$
2. $\text{a capacitance of reactance } X_C = X_L \text{ is included in the same circuit.}$
3. $\text{an iron rod is inserted in the coil.}$
4. $\text{frequency of the AC source is decreased.}$

Solution:

$\text{The brightness of the bulb decreases when the current in the circuit decreases.}$ $\text{The current through the } LR \text{ circuit is given by:}$ $I = \frac{E}{\sqrt{\omega^2 L^2 + R^2}}$ $\text{If inductance increases, the current will decrease.}$ $\text{The inductance can be increased by increasing the number of turns or by inserting an iron rod in the coil.}$ $\text{Hence, option (3) is the correct answer.}$

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
}