Import Question JSON

Current Question (ID: 20140)

Question:

$\text{The equivalent capacitance between points A and B in the figure (shown below) will be:}$ $\begin{array}{c} \text{A} \; \text{---} \; \text{8} \, \mu\text{F} \; \text{---} \; \text{8} \, \mu\text{F} \; \text{---} \; \text{8} \, \mu\text{F} \; \text{---} \; \text{8} \, \mu\text{F} \; \text{---} \; \text{8} \, \mu\text{F} \; \text{---} \; \text{B} \end{array}$

Options:

1. $2 \, \mu\text{F}$
2. $4 \, \mu\text{F}$
3. $6 \, \mu\text{F}$
4. $8 \, \mu\text{F}$

Solution:

$\text{Hint: Recall the combination of capacitors.}$ $\text{Step 1: Redraw the equivalent circuit diagram.}$ $\text{Step 2: Find the equivalent capacitance between points A and B.}$ $C_{\text{eq}} = \frac{C_1 C_2}{C_1 + C_2}$ $= \frac{3C \times C}{2C + C}$ $= \frac{3}{4} C$ $= 6 \, \mu\text{F}$

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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
}