Import Question JSON

Current Question (ID: 16696)

Question:

$\text{Two batteries, one of emf } 18 \text{ V and internal resistance } 2 \ \Omega \text{ and the other of emf } 12 \text{ V and internal resistance } 1 \ \Omega, \text{ are connected as shown. Reading of the voltmeter is:}$ $\text{(if a voltmeter is ideal)}$

Options:

1. $14 \text{ V}$
2. $15 \text{ V}$
3. $18 \text{ V}$
4. $30 \text{ V}$

Solution:

$\text{Hint: The cells are in parallel combination.}$ $\text{Step: Find the reading of the voltmeter.}$ $\text{The net EMF } \varepsilon_{\text{eq}} \text{ of the circuit is given by:}$ $\varepsilon_{\text{eq}} = \frac{\varepsilon_1 r_2 + \varepsilon_2 r_1}{r_1 + r_2}$ $\varepsilon_{\text{eq}} = \frac{18 \times 1 + 12 \times 2}{1 + 2}$ $\Rightarrow \varepsilon_{\text{eq}} = \frac{42}{3} = 14 \text{ V}$ $\text{The reading of the voltmeter is given by:}$ $\text{The reading of the voltmeter } = \varepsilon_{\text{eq}} = 14 \text{ V}$ $\text{Hence, option (1) is the correct answer.}$

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
}