Two electric lamps have filaments of the same metal having the same thickness. If one of them gives 100 watt and other gives 500 watt across the same supply, then: 

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SSC JE Electrical 14 Nov 2022 Shift 3 Official Paper
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  1. 100 watt lamp filament has longer a length
  2. 100 watt lamp filament has a shorter length
  3. 100 watt and 500 watt lamp filaments have the same length
  4. 500 watt lamp filament has a longer length

Answer (Detailed Solution Below)

Option 1 : 100 watt lamp filament has longer a length
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Detailed Solution

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Concept

When two lamps are connected in parallel (same supply), the power of each lamp is given by:

The resistance is given by:

where, ρ = Resistivity

l = Length

A = Area

Calculation

From the above expression, for the same metal having the same thickness, the power is inversely proportional to length.

Hence, a 100-watt lamp filament has a longer length than a 500-watt lamp.

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