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Current Question (ID: 16567)

Question:

$\text{A capacitor of } 1 \, \mu\text{F} \text{ withstands a maximum voltage of } 6 \text{ kilovolts while another capacitor of } 2 \, \mu\text{F} \text{ withstands a maximum voltage of } 4 \text{ kilovolts. If the two capacitors are connected in series, the system will withstand a maximum voltage of:}$

Options:

1. $2 \, \text{kV}$
2. $4 \, \text{kV}$
3. $6 \, \text{kV}$
4. $9 \, \text{kV}$

Solution:

$\text{For series combination, } C_s = \frac{C_1 C_2}{C_1 + C_2} \Rightarrow C_s = \frac{2}{3} \, \mu\text{F}$ $\text{When connected in series, the maximum charge that can flow through the combination equals the lower value of charge accommodated by the first capacitor i.e. } 6000 \, \mu\text{C.}$ $\therefore Q_1 = 6000 \, \mu\text{C and } 8000 \, \mu\text{C}$ $V_s = \frac{Q_1}{C_s} = \frac{6000 \, \mu\text{C}}{(2/3) \, \mu\text{C}} \Rightarrow V_s = 9 \, \text{kV}$

Import JSON File

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
}