Import Question JSON

Current Question (ID: 17333)

Question:

$\text{The AC source in the circuit shown in the figure produces a voltage}$ $V = 20 \cos(2000t) \text{ volts. Neglecting source resistance, the voltmeter and ammeter readings will be (approximately):}$

Options:

1. $4 \text{ V, } 2.0 \text{ A}$
2. $0 \text{ V, } 2 \text{ A}$
3. $5.6 \text{ V, } 1.4 \text{ A}$
4. $8 \text{ V, } 2.0 \text{ A}$

Solution:

$\text{Hint: } i_{\text{rms}} = \frac{v_{\text{rms}}}{z}$ $\text{Step: Find the reading of the voltmeter and ammeter.}$ $X_L = \omega L = 2000 \times 5 \times 10^{-3} = 10 \ \Omega$ $X_C = \frac{1}{\omega C} = \frac{1}{2000 \times 50 \times 10^{-6}} = 10 \ \Omega$ $\Rightarrow X_C = X_L \text{ So, it is a case of resonance.}$ $Z = \sqrt{R^2 + (X_L - X_C)^2} = 10 \ \Omega$ $\Rightarrow I = \frac{V}{R} = \frac{20}{\sqrt{2} \times 10} = \frac{\sqrt{2}}{2} = 1.4 \ \text{A}$ $\Rightarrow V = IR = 1.4 \times 4 = 5.6 \ \text{V}$ $\text{Hence, option (3) is the correct answer.}$

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
}