Directions: In the following questions, a statement of assertion (A) ...
Assertion: When current through a bulb decreases by 0.5%, the glow of the bulb decreases by 1%.
Reason: Glow (Power) is directly proportional to the square of the current.
The correct answer is option 'B': Both the assertion (A) and reason (R) are true, but the reason (R) is not the correct explanation of the assertion (A).
Explanation:
The assertion claims that when the current through a bulb decreases by 0.5%, the glow of the bulb decreases by 1%. The reason stated is that the glow or power of the bulb is directly proportional to the square of the current.
However, this assertion and reason do not align with the actual relationship between current and power in a bulb. Let's break down the explanation to understand why:
1. Relationship between current and power:
The power (glow) of a bulb is given by the equation P = I^2 * R, where P is the power, I is the current, and R is the resistance of the bulb. From this equation, it is clear that power is directly proportional to the square of the current.
2. Impact of a 0.5% decrease in current:
If the current through a bulb decreases by 0.5%, the new current would be 99.5% of the original current. Let's denote the original current as I and the new current as I'.
I' = 0.995 * I
3. Impact on the power (glow) of the bulb:
Substituting the new current (I') into the power equation, we get:
P' = (I')^2 * R
= (0.995 * I)^2 * R
= (0.995)^2 * I^2 * R
= 0.990025 * I^2 * R
Comparing this with the original power (P = I^2 * R), we can see that the power (glow) of the bulb decreases by approximately 0.9975% (1 - 0.990025) when the current decreases by 0.5%.
Conclusion:
Based on the above analysis, we can conclude that the statement of reason (R) is not the correct explanation for the assertion (A). The actual decrease in the glow of the bulb is approximately 0.9975% when the current decreases by 0.5%, which does not align with the assertion that the decrease in glow is 1%.
Therefore, option 'B' is the correct answer.
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