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Current Question (ID: 20235)

Question:

$\text{A meter bridge setup is shown in the figure. It is used to determine an unknown resistance } R \text{ using a given resistor of } 15 \, \Omega. \text{ The galvanometer } (G) \text{ shows a null deflection when the tapping key is at } 43 \, \text{cm mark from end } A. \text{ If the end correction for end } A \text{ is } 2 \, \text{cm, then the determined value of } R \text{ will be:}$

Options:

1. $19 \, \Omega$
2. $22 \, \Omega$
3. $25 \, \Omega$
4. $28 \, \Omega$

Solution:

$\text{Hint: } \frac{R}{S} = \frac{l}{100-l}$ $\text{Using the conditions of a balanced wheat stone bridge and adding the end correction.}$ $\frac{15}{(43 + 2)} = \frac{R}{(102 - 45)} \Rightarrow R = \frac{57}{45} \times 15$ $R = 19 \, \Omega$

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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
}