Import Question JSON

Current Question (ID: 16701)

Question:

$\text{Eels are able to generate current with biological cells called electroplaques.}$ $\text{The electroplaques in an eel are arranged in 100 rows, each row stretching}$ $\text{horizontally along the body of the fish containing 5000 electroplaques.}$ $\text{The arrangement is suggestively shown below. Each electroplaque has an emf of}$ $0.15 \text{ V and internal resistance of } 0.25 \ \Omega.$ $\text{The water surrounding the eel completes a circuit between the head and its}$ $\text{tail. If the water surrounding it has a resistance of } 500 \ \Omega, \text{ the current an eel}$ $\text{can produce in water is about:}$

Options:

1. $1.5 \text{ A}$
2. $3.0 \text{ A}$
3. $15 \text{ A}$
4. $30 \text{ A}$

Solution:

$\text{(1) Given problem is the case of mixed grouping of cells}$ $\text{So total current produced } i = \frac{nE}{R + nr}$ $\text{Where, } m = \text{number of rows and } n = \text{number of cells}$ $\text{Here } m = 100, \ n = 5000, \ R = 500 \ \Omega$ $E = 0.15 \text{ V and } r = 0.25 \ \Omega$ $\Rightarrow i = \frac{5000 \times 0.15}{500 + \frac{5000 \times 0.25}{100}} = \frac{750}{512.5} \approx 1.5 \text{ A}$

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
}