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Current Question (ID: 20207)

Question:

$\text{A potentiometer } PQ \text{ is set up to compare two resistances as shown in the figure. The ammeter } A \text{ in the circuit reads } 1.0 \text{ A when the two-way key } K_3 \text{ is open. The balance point is at a length } l_1 \text{ cm from } P \text{ when the two-way key } K_3 \text{ is plugged in between } 2 \text{ and } 1, \text{ while the balance point is at a length } l_2 \text{ cm from } P \text{ when the key } K_3 \text{ is plugged in between } 3 \text{ and } 1. \text{ The ratio of two resistances } \frac{R_1}{R_2}, \text{ is found to be:}$

Options:

1. $\frac{l_1}{l_1 + l_2}$
2. $\frac{l_2}{l_2 - l_1}$
3. $\frac{l_1}{l_1 - l_2}$
4. $\frac{l_1}{l_2 - l_1}$

Solution:

$\text{Hint: } V = IR, V = xl$

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
}