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Current Question (ID: 20572)

Question:

$\text{An LCR circuit contains resistance of } 110 \, \Omega \text{ and a supply of } 220 \, \text{V at } 300 \, \text{rad/s angular frequency.}$ $\text{If only capacitance is removed from the circuit, current lags behind the voltage by } 45^\circ.$ $\text{If on the other hand, only inductor is removed the current leads by } 45^\circ \text{ with the applied voltage.}$ $\text{The rms current flowing in the circuit will be:}$

Options:

1. $1 \, \text{A}$
2. $2.5 \, \text{A}$
3. $1.5 \, \text{A}$
4. $2 \, \text{A}$

Solution:

$\text{Hint: } I_{\text{rms}} = \frac{V_{\text{rms}}}{R}$

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
}