Import Question JSON

Current Question (ID: 20203)

Question:

$A \ 10 \ \text{V} \ \text{battery with internal resistance} \ 1 \ \Omega \ \text{and a} \ 15 \ \text{V battery with internal resistance} \ 0.6 \ \Omega \ \text{are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be:}$

Options:

1. $11.9 \ \text{V}$
2. $13.1 \ \text{V}$
3. $12.5 \ \text{V}$
4. $24.5 \ \text{V}$

Solution:

$\text{Hint: Use Kirchhoff's voltage law in the circuit}$ $\text{Step 1: Find the current through the circuit.}$ $\text{Applying Kirchhoff's voltage law in the loop BCDE.}$ $\Rightarrow 15 - 10 - (1 \times i) - (0.6 \times i) = 0$ $\Rightarrow 1.6 \ i = 5$ $\Rightarrow i = \frac{5}{1.6} = 3.125 \ \text{A}$ $\text{Step 2: Find the reading in the voltmeter}(V).$ $\text{Now, applying Kirchhoff's voltage law in the loop ABEF.}$ $\Rightarrow V - 15 + (0.6 \times i) = 0$ $\Rightarrow V - 15 + (0.6 \times 3.125) = 0$ $\Rightarrow V = 13.125 \ \text{V}$ $\text{Hence, option (2) is the correct answer.}$

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
}