Import Question JSON

Current Question (ID: 17301)

Question:

$\text{An ideal resistance } R, \text{ ideal inductance } L, \text{ ideal capacitance } C, \text{ and AC voltmeters } V_1, V_2, V_3 \text{ and } V_4 \text{ are connected to an AC source as shown. At resonance:}$

Options:

1. $\text{reading in } V_3 = \text{reading in } V_1$
2. $\text{reading in } V_1 = \text{reading in } V_2$
3. $\text{reading in } V_2 = \text{reading in } V_4$
4. $\text{reading in } V_2 = \text{reading in } V_3$

Solution:

$\text{Hint: At resonance, } V_C = V_L.$ $\text{Step: Find the voltage across the series LCR circuit.}$ $\text{At resonance, } V_C = V_L.$ $\Rightarrow V_2 = V_3$ $\text{For the series } LCR \text{ combination, we know that;}$ $V_N = \sqrt{V_R^2 + (V_L - V_C)^2}$ $\Rightarrow V_N = V_R$ $\text{The voltage across the series } LCR \text{ circuit is given by;}$ $\Rightarrow V_4 = V_R = V_1$ $\text{Hence, option (4) is the correct answer.}$

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
}