Import Question JSON

Current Question (ID: 16698)

Question:

$\text{A current of } 2 \text{ A is to be sent through a resistor of } 5 \, \Omega. \text{ Number of cells required in series, if each has emf } 2 \text{ V and internal resistance } 0.5 \, \Omega, \text{ are:}$

Options:

1. $40$
2. $30$
3. $20$
4. $10$

Solution:

$\text{Hint: In series combination, } \varepsilon_{\text{net}} = \varepsilon_1 + \varepsilon_2 + \varepsilon_3 + \ldots$ $\text{Step 1: Find the net resistance.}$ $R_{\text{net}} = R + r_1 + r_2 + r_3 + \ldots \text{ n times} = R + nr$ $\text{Step 2: Find the current in the circuit.}$ $i = \frac{\varepsilon_1 + \varepsilon_2 + \varepsilon_3 + \ldots \text{ n times}}{R + nr}$ $i = \frac{n\varepsilon}{R + nr}$ $2 = \frac{n \times 2}{R + n \times 0.5}$ $R + n \times 0.5 = \frac{2n}{2} = n$ $R = 0.5n$ $n = \frac{R}{0.5} = \frac{5}{0.5} = 10$

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
}