Import Question JSON

Current Question (ID: 20560)

Question:

$\text{Given below are two statements:}$ $\text{Statement I: In a purely inductive circuit, the average power consumed is very high.}$ $\text{Statement II: In a purely inductive circuit only, resonance can be achieved.}$

Options:

1. $\text{Both Statement I and Statement II are correct.}$
2. $\text{Statement I is incorrect and Statement II is correct.}$
3. $\text{Statement I is correct and Statement II is incorrect.}$
4. $\text{Both Statement I and Statement II are incorrect.}$

Solution:

$\text{Hint: In a purely inductive circuit } \cos \phi = 0.$ $\text{Explanation: In a purely inductive circuit, the current lags the voltage by } 90^\circ. \text{ The average power consumed is given by:}$ $V_{\text{rms}} I_{\text{rms}} \cos \phi = V_{\text{rms}} I_{\text{rms}} \cos 90^\circ = 0. \text{ Therefore, statement I is false.}$ $\text{Resonance in an AC circuit occurs when the inductive reactance } (X_L) \text{ of the inductor and the capacitive reactance } (X_C) \text{ of a capacitor cancel each other, resulting in a purely resistive impedance.}$ $\text{While other AC circuits with both inductor and capacitor can achieve resonance, a purely inductive circuit cannot.}$ $\text{Therefore, the resonance is achieved in } LCR \text{ circuits not in purely inductive or capacitive circuits.}$ $\text{Therefore, statement II is false.}$ $\text{Therefore, both Statement I and Statement II are incorrect.}$ $\text{Hence, option (4) is the correct answer.}$

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
}