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Current Question (ID: 16636)

Question:

$\text{In the circuit shown in the figure, the effective resistance between } A \text{ and } B \text{ is:}$

Options:

1. $2 \, \Omega$
2. $4 \, \Omega$
3. $6 \, \Omega$
4. $8 \, \Omega$

Solution:

$8 \, \Omega \text{ and } 8 \, \Omega \text{ are in parallel.}$ $\Rightarrow \frac{1}{R_1} = \frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4} \Rightarrow R_1 = 4 \, \Omega$ $4 \, \Omega \text{ and } 4 \, \Omega \text{ are also in parallel.}$ $\Rightarrow \frac{1}{R_2} = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \Rightarrow R_2 = 2 \, \Omega$ $\text{Now, } R_1 \text{ and } R_2 \text{ are in series.}$ $\Rightarrow R_3 = R_1 + R_2 = 4 + 2 = 6 \, \Omega$ $\text{Now, } 6 \, \Omega, R_3 \text{ and } 6 \, \Omega \text{ are in parallel.}$ $\Rightarrow \frac{1}{R_{\text{net}}} = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$ $\Rightarrow R_{\text{net}} = 2 \, \Omega$

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Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

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
}