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Current Question (ID: 20420)

Question:

$\text{A } 72 \, \Omega \text{ galvanometer is shunted by a resistance of } 8 \, \Omega. \text{ The percentage of the total current that passes through the galvanometer is:}$ $1. \; 0.1\%$ $2. \; 10\%$ $3. \; 25\%$ $4. \; 0.25\%$

Options:

1. 0.1\%
2. 10\%
3. 25\%
4. 0.25\%

Solution:

$\text{Hint: } S = \frac{R_G}{I_g - 1}$ $\text{Step: Find the percentage of the total current passing through the galvanometer.}$ $\text{The current passing through the galvanometer is given by:}$ $\Rightarrow \; I_G = \frac{I \times R}{R + R_G}$ $\text{The percentage of the total current passing through the galvanometer is given by:}$ $\Rightarrow \; \frac{I_G}{I} \% = \frac{R \times 100}{R + R_G}$ $\Rightarrow \; \frac{I_G}{I} \% = \frac{8 \times 100}{8 + 72} \Rightarrow 10\%$ $\text{Hence, option (2) is the correct answer.}$

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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
}