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Current Question (ID: 17290)

Question:

$\text{In a series } RLC \text{ circuit, potential differences across } R, L \text{ and } C \text{ are } 30 \text{ V}, 60 \text{ V and } 100 \text{ V respectively, as shown in the figure. The emf of the source (in volts) will be:}$

Options:

1. $190$
2. $70$
3. $50$
4. $40$

Solution:

$\text{In a series } RLC \text{ circuit, the total emf is the vector sum of the potential differences across } R, L, \text{ and } C.$ $\text{Since they are in series, the potential differences add up algebraically:}$ $E = V_R + V_L + V_C = 30 + 60 + 100 = 190 \text{ V}$

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
}