Two electric bulbs marked 100 W, 220 V and 200 W, 220 V have tungsten filaments of the same length. Which bulb has a thicker filament?

The resistance of a filament is given by Ohm’s law:

R=V2/P

where:

  • V=220V (same for both bulbs),
  • P is the power rating.

Step 1: Calculate the Resistance of Each Bulb

For the 100 W bulb:

R1=2202/100=48400/100=484 Ω

For the 200 W bulb:

R2=2202/200=48400/200=242 Ω

Step 2: Relationship Between Resistance and Thickness

The resistance of a wire is given by:

R=ρ.L/A

where:

  • ρ is the resistivity of tungsten (same for both filaments),
  • L is the length of the filament (same for both, as stated in the problem),
  • A is the cross-sectional area (which determines thickness).

Rearranging for :

A=ρ.L/R

Since R2<R1, the 200 W bulb has a lower resistance, meaning A2>A1. Since the cross-sectional area is directly related to thickness, the 200 W bulb has a thicker filament.

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