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Current Question (ID: 16856)

Question:

$\text{When a } 12 \, \Omega \text{ resistor is connected in parallel with a moving coil galvanometer, its deflection reduces from } 50 \text{ divisions to } 10 \text{ divisions. What will be the resistance of the galvanometer?}$ $1. \, 24 \, \Omega$ $2. \, 36 \, \Omega$ $3. \, 48 \, \Omega$ $4. \, 60 \, \Omega$

Options:

1. $24 \, \Omega$
2. $36 \, \Omega$
3. $48 \, \Omega$
4. $60 \, \Omega$

Solution:

$\text{Hint: } S = \left( \frac{I_g}{i - I_g} \right) R_G$ $\text{Step: Find the resistance of the galvanometer.}$ $\text{The shunt resistance of the galvanometer is given by:}$ $S = \left( \frac{I_g}{i - I_g} \right) R_G$ $\Rightarrow \, 12 = \left( \frac{10}{50 - 10} \right) \times R_G$ $\Rightarrow \, R_G = \frac{12 \times 40}{10} = 48 \, \Omega$ $\text{Hence, option (3) is the correct answer.}$

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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
}