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Current Question (ID: 16690)

Question:

$\text{A cell having an emf } \varepsilon \text{ and internal resistance } r \text{ is connected across a variable external resistance } R. \text{ As the resistance } R \text{ is increased, the plot of potential difference } V \text{ across } R \text{ is given by:}$

Options:

1. $\text{Graph 1}$
2. $\text{Graph 2}$
3. $\text{Graph 3}$
4. $\text{Graph 4}$

Solution:

$\text{Hint: } I = \frac{\varepsilon}{R+r}$ $\text{Step: Identify the plot of potential differences } V \text{ across } R.$ $\text{The current in the circuit is given by:}$ $I = \frac{\varepsilon}{R+r}$ $\text{The potential difference across } R, \text{ is given by:}$ $V = IR = \left(\frac{\varepsilon}{R+r}\right)R$ $\Rightarrow V = \frac{\varepsilon}{1+\frac{r}{R}}$ $\text{When } R = 0, V = 0$ $R = \infty, V = \varepsilon$ $\text{The graph of } V \text{ against } R \text{ will start at the origin } (0, 0) \text{ and will asymptotically approach } E. \text{ This indicates that the graph is not a straight line but a curve that rises and flattens out as } R \text{ increases.}$

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
}