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Current Question (ID: 20359)

Question:

$\text{A galvanometer of resistance } G \text{ is converted into a voltmeter of range } 0-1 \text{ V by connecting a resistance } R_1 \text{ in series with it. The additional resistance that should be connected in series with } R_1 \text{ to increase the range of the voltmeter to } 0-2 \text{ V will be:}$ $1. \ R_1$ $2. \ R_1 + G$ $3. \ R_1 - G$ $4. \ G$

Options:

1. $R_1$
2. $R_1 + G$
3. $R_1 - G$
4. $G$

Solution:

$\text{Hint: } V = I (G + R_1)$ $\Rightarrow 1 = i_g (G + R_1) \quad \ldots (1)$ $\Rightarrow 2 = i_g (R_1 + R_2 + G) \quad \ldots (2)$ $(1) \% (2)$ $\Rightarrow \frac{1}{2} = \frac{G + R_1}{G + R_1 + R_2}$ $G + R_1 + R_2 = 2G + 2h_1$ $(R_2 = G + R_1)$

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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
}