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Two electric bulbs have tungsten filament of the same length but of different radii if the bulbs are of wattage 40 watt and 60 watt and the radii of their filaments R1 and R2 respectively then?
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Two electric bulbs have tungsten filament of the same length but of di...
Comparing Filament Radii of Two Electric Bulbs
Electric bulbs with different wattages (40W and 60W) have tungsten filaments of the same length but different radii (R1 and R2). Let's analyze the relationship between the radii and wattages of the bulbs.
Understanding the Power-Radii Relationship
- The power (wattage) of an electric bulb is directly proportional to the fourth power of the radius of its filament.
- Mathematically, P ∝ R^4, where P is the power and R is the radius of the filament.
Comparing the Two Bulbs
- For the 40W bulb: P1 = 40W and radius R1.
- For the 60W bulb: P2 = 60W and radius R2.
Using the Power-Radii Relationship
- Since the length of the filaments is the same, we can set up a ratio of the powers to determine the relationship between the radii.
- (P2/P1) = (R2^4 / R1^4) = (60/40)
- R2^4 / R1^4 = 1.5
- R2 / R1 = (1.5)^(1/4) ≈ 1.12
Calculating the Radii
- If we assume the radius of the filament in the 40W bulb (R1) is 1 unit, then the radius of the filament in the 60W bulb (R2) would be approximately 1.12 units.
Conclusion
- The radii of the filaments in the two electric bulbs are in a ratio of approximately 1:1.12, with the larger radius corresponding to the higher wattage bulb.
Electric bulbs with different wattages (40W and 60W) have tungsten filaments of the same length but different radii (R1 and R2). Let's analyze the relationship between the radii and wattages of the bulbs.
Understanding the Power-Radii Relationship
- The power (wattage) of an electric bulb is directly proportional to the fourth power of the radius of its filament.
- Mathematically, P ∝ R^4, where P is the power and R is the radius of the filament.
Comparing the Two Bulbs
- For the 40W bulb: P1 = 40W and radius R1.
- For the 60W bulb: P2 = 60W and radius R2.
Using the Power-Radii Relationship
- Since the length of the filaments is the same, we can set up a ratio of the powers to determine the relationship between the radii.
- (P2/P1) = (R2^4 / R1^4) = (60/40)
- R2^4 / R1^4 = 1.5
- R2 / R1 = (1.5)^(1/4) ≈ 1.12
Calculating the Radii
- If we assume the radius of the filament in the 40W bulb (R1) is 1 unit, then the radius of the filament in the 60W bulb (R2) would be approximately 1.12 units.
Conclusion
- The radii of the filaments in the two electric bulbs are in a ratio of approximately 1:1.12, with the larger radius corresponding to the higher wattage bulb.
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Two electric bulbs have tungsten filament of the same length but of different radii if the bulbs are of wattage 40 watt and 60 watt and the radii of their filaments R1 and R2 respectively then?
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Two electric bulbs have tungsten filament of the same length but of different radii if the bulbs are of wattage 40 watt and 60 watt and the radii of their filaments R1 and R2 respectively then? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two electric bulbs have tungsten filament of the same length but of different radii if the bulbs are of wattage 40 watt and 60 watt and the radii of their filaments R1 and R2 respectively then? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two electric bulbs have tungsten filament of the same length but of different radii if the bulbs are of wattage 40 watt and 60 watt and the radii of their filaments R1 and R2 respectively then?.
Two electric bulbs have tungsten filament of the same length but of different radii if the bulbs are of wattage 40 watt and 60 watt and the radii of their filaments R1 and R2 respectively then? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two electric bulbs have tungsten filament of the same length but of different radii if the bulbs are of wattage 40 watt and 60 watt and the radii of their filaments R1 and R2 respectively then? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two electric bulbs have tungsten filament of the same length but of different radii if the bulbs are of wattage 40 watt and 60 watt and the radii of their filaments R1 and R2 respectively then?.
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