Import Question JSON

Current Question (ID: 16659)

Question:

$\text{A current of } 3 \text{ A flows through the } 2 \, \Omega \text{ resistor shown in the circuit. The power dissipated in the } 5 \, \Omega \text{ resistor is:}$

Options:

1. $4 \, \text{W}$
2. $2 \, \text{W}$
3. $1 \, \text{W}$
4. $5 \, \text{W}$

Solution:

$\text{Hint: The potential difference in the parallel branches remains same.}$ $\text{Step 1: Find the potential drop across } 2 \, \Omega \text{ resistor.}$ $\text{Using, } V = IR$ $\text{The voltage across } 2 \, \Omega \text{ resistor } V = 2 \times 3 = 6 \, \text{V}$ $\text{Step 2: Find the current in the lower branch.}$ $\text{The voltage across the lowest arm containing } 1 \, \Omega \text{ and } 5 \, \Omega \text{ will also be } 6 \, \text{V.}$ $\text{The net current across } 5 \, \Omega \text{ will be given by;}$ $V = IR \Rightarrow I = \frac{V}{R}$ $I = \frac{6}{(1+5)} \Rightarrow I = 1 \, \text{A}$ $\text{Step 3: Find the power dissipated in } 5 \, \Omega \text{ resistance.}$ $\text{Therefore, the power across } 5 \, \Omega,$ $P = I^2R \Rightarrow P = ((1)^2 \times 5) \, \text{W} = 5 \, \text{W}$ $\text{Hence, option (4) is the correct answer.}$

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
}