Import Question JSON

Current Question (ID: 16669)

Question:

$\text{An electric heater consists of a nichrome coil and operates under } 220 \text{ V, consuming } 1 \text{ kW of power. Part of its coil burned out and was reconnected after removing the burnt portion. The power it will consume now is:}$

Options:

1. $\text{more than } 1 \text{ kW}$
2. $\text{less than } 1 \text{ kW but not zero}$
3. $1 \text{ kW}$
4. $\text{zero}$

Solution:

$\text{Hint: A part of the coil burned then resistance decreased.}$ $\text{Step: Find the power consumed by the electric heater.}$ $\text{The resistance of the coil is given by:}$ $\Rightarrow R = \rho \frac{l}{A}$ $\text{Therefore, after cutting off the burnt portion, resistance will decrease.}$ $\text{The power consumed by the electric heater is given by:}$ $\text{As } P = \frac{V^2}{R}$ $\Rightarrow P \propto \frac{1}{R}$ $\text{Therefore, the power will consume more than } 1 \text{ kW.}$ $\text{Hence, option (1) is the correct answer.}$

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
}