Import Question JSON

Current Question (ID: 16678)

Question:

$\text{Given below are two statements:}$ $\text{Assertion (A):}$ \text{A } 60 \text{ W } - 220 \text{ V bulb glows more than a } 100 \text{ W } - 220 \text{ V bulb when they are connected in series across a potential difference.}$ $\text{Reason (R):}$ \text{When they are connected in series, the resistance of the } 100 \text{ W bulb will be more.}$

Options:

1. $\text{Both (A) and (R) are True and (R) is the correct explanation of (A).}$
2. $\text{Both (A) and (R) are True but (R) is not the correct explanation of (A).}$
3. $\text{(A) is True but (R) is False.}$
4. $\text{Both (A) and (R) are False.}$

Solution:

$\text{Hint: } P = \frac{V^2}{R}$ $\text{Step 1: Find the resistance of the two bulbs.}$ $\text{Using } P = \frac{V^2}{R} \Rightarrow R = \frac{V^2}{P} \ldots (1)$ $\text{Substituting the values of the first bulb in the equation (1), we get;}$ $\Rightarrow R = \frac{V^2}{P} \Rightarrow R_{60} = \frac{(220)^2}{60}$ $\text{Substituting the values of the second bulb in the equation (1), we get;}$ $\Rightarrow R = \frac{V^2}{P} \Rightarrow R_{100} = \frac{(220)^2}{100}$ $\text{Step 2: Compare the power of the two bulbs.}$ $\text{Since the bulbs are in series, the current will be the same in both.}$ $\text{Power in the bulbs is given by; } P = I^2R \ldots (2)$ $\text{Substituting the value of the first bulb in equation (2), we get;}$ $\Rightarrow P_{60} = I^2R_{60} \Rightarrow P_{60} = I^2 \frac{(220)^2}{60}$ $\text{Substituting the value of the second bulb in equation (2), we get;}$ $\Rightarrow P_{100} = I^2R_{100} \Rightarrow P_{100} = I^2 \frac{(220)^2}{100}$ $\text{Thus, } P_{60} > P_{100}$ $\text{Therefore, (A) is true but (R) is false.}$ $\text{Hence, option (3) is the correct answer.}$

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
}