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Current Question (ID: 20229)

Question:

$\text{A cell } E_1 \text{ of emf } 6 \text{ V and internal resistance } 2 \, \Omega \text{ is connected with another cell } E_2 \text{ of emf } 4 \text{ V and internal resistance } 8 \, \Omega \text{ (as shown in the figure). The potential difference across points } X \text{ and } Y \text{ is:}$

Options:

1. $10 \, \text{V}$
2. $3.6 \, \text{V}$
3. $5.6 \, \text{V}$
4. $2 \, \text{V}$

Solution:

$\text{Hint: Apply KVL in the loop.}$ $\text{Step 1: Find the current in the circuit.}$ $\text{Apply KVL in the loop as shown in the above figure we get:}$ $-4 - 8i + 6 - 2i = 0$ $\Rightarrow i = 0.2 \, \text{A}$ $\text{Step 2: Find the potential difference between the given points.}$ $V_y - V_x = 4 + 8i = 4 + 8 \times 0.2$ $\Rightarrow V_y - V_x = 5.6 \, \text{V}$ $\text{Hence, option (3) is the correct answer.}$

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
}