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Current Question (ID: 16635)

Question:

$\text{A potential divider is used to give outputs of } 2 \text{ V and } 3 \text{ V from a } 5 \text{ V source, as shown in the figure.}$ $\text{Which combination of resistances, from the ones given below, } R_1, R_2, \text{ and } R_3 \text{ give the correct voltages?}$

Options:

1. $R_1 = 1 \text{ k}\Omega, R_2 = 1 \text{ k}\Omega, R_3 = 2 \text{ k}\Omega$
2. $R_1 = 2 \text{ k}\Omega, R_2 = 1 \text{ k}\Omega, R_3 = 2 \text{ k}\Omega$
3. $R_1 = 1 \text{ k}\Omega, R_2 = 2 \text{ k}\Omega, R_3 = 2 \text{ k}\Omega$
4. $R_1 = 3 \text{ k}\Omega, R_2 = 2 \text{ k}\Omega, R_3 = 2 \text{ k}\Omega$

Solution:

$\text{The total resistance } R = R_1 + R_2 + R_3 = 5 \text{ k}\Omega.$ $\text{The voltage across } R_3 \text{ is } V_3 = \frac{R_3}{R} \times 5 \text{ V} = \frac{2}{5} \times 5 \text{ V} = 2 \text{ V}.$ $\text{The voltage across } R_2 \text{ is } V_2 = \frac{R_2}{R} \times 5 \text{ V} = \frac{1}{5} \times 5 \text{ V} = 1 \text{ V}.$ $\text{Thus, the voltage across } R_1 + R_2 \text{ is } 3 \text{ V}.$ $\text{Therefore, the correct combination is option 2.}$

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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
}