Import Question JSON

Current Question (ID: 16560)

Question:

$\text{Five identical plates each of area } A \text{ are joined as shown in the figure.}$ $\text{The distance between the plates is } d. \text{ The plates are connected to a potential}$ $\text{difference of } V \text{ volts. The charge on plates 1 and 4 will be:}$

Options:

1. $\frac{\varepsilon_0 A V}{d}, \frac{2 \varepsilon_0 A V}{d}$
2. $\frac{2 \varepsilon_0 A V}{d}, \frac{\varepsilon_0 A V}{d}$
3. $\frac{\varepsilon_0 A V}{d}, -\frac{2 \varepsilon_0 A V}{d}$
4. $-\frac{\varepsilon_0 A V}{d}, \frac{\varepsilon_0 A V}{d}$

Solution:

$\text{(3) The given circuit can be redrawn as follows. All capacitors are identical}$ $\text{and each having capacitance } C = \frac{\varepsilon_0 A}{d}$ $|\text{Charge on each capacitor}| = |\text{Charge on each plate}|$ $= \frac{\varepsilon_0 A}{d} V$ $\text{Plate 1 is connected with positive terminal of battery so charge on it will be}$ $+\frac{\varepsilon_0 A}{d} V$ $\text{Plate 4 comes twice and it is connected with negative terminal of battery, so}$ $\text{charge on plate 4 will be } -\frac{2 \varepsilon_0 A}{d} V$

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
}