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Current Question (ID: 16671)

Question:

$\text{Four identical bulbs } A, B, C \text{ and } D \text{ are connected in a circuit as shown in the figure.}$ $\text{Now whenever any bulb fails, then it cannot conduct current through it.}$ $\text{Then which of the following statement(s) is/are true?}$

Options:

1. $(i) \text{ only}$
2. $(ii) \text{ only}$
3. $(i) \text{ and } (ii) \text{ only}$
4. $(ii) \text{ and } (iii) \text{ only}$

Solution:

$\text{Hint: Bulb, D is short-circuited.}$ $\text{Step: Find the power consumed by the bulbs.}$ $\text{The power consumed by the bulbs is given by;}$ $P = \frac{V^2}{R}$ $\text{As the resistance of each bulb is the same, therefore, power across the bulb}$ $\text{will be directly proportional to the square of potential difference i.e.,}$ $P \propto V^2$ $\text{The voltage across each bulb is shown in the figure below;}$ $V_C > V_A = V_B$ $\Rightarrow P_C > P_A$ $\text{The brightness of bulb } C \text{ is the highest.}$ $\text{If } A \text{ fails, there will be no current through } AB \text{ and } B \text{ will not glow.}$ $\text{When } C \text{ fails, it wouldn't affect } D \text{ unless there's some shared current path}$ $\text{that could increase the current through } D. \text{ However, for identical bulbs in}$ $\text{parallel, the failure of one bulb would generally not increase the brightness}$ $\text{of the other bulbs significantly.}$ $\text{Therefore, statements i and ii are true.}$ $\text{Hence, option (3) is the correct answer.}$

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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
}