Correct Answer  Option 1 : 80 W filament is thicker
The correct answer is option 1) i.e. 80 W filament is thicker
CONCEPT:

Power: The rate of work done by an electric current is called power. It is denoted by P. The SI unit of power is the watt (W).

Power dissipation is given by:
\(\Rightarrow P = VI = V.\frac{V}{R} = \frac{V^2}{R}\)
Where V is the potential difference across resistance, I is current flowing and R is resistance.

The resistivity of a material is defined as the resistance offered by a material of unit crosssectional area and unit length.
 It is represented as
\(\Rightarrow ρ = \frac{RA}{l}\)
Where R is the resistance,l is the length of the material and A is the area of crosssection.
 Resistivity is an intrinsic property i.e. it is the same for a given type of material.
EXPLANATION:
We know, \(P =\frac{V^2}{R}\) and \(ρ = \frac{RA}{l}\)
⇒ \(P =\frac{V^2A}{ρ l}\)
Assuming that both the bulb filaments are made of the same material, their resistivities (ρ) are the same.
If connected in the same circuit, the voltage drop V across the bulbs also remains the same.
Given that the length (l) of the filaments are the same ⇒ P ∝ A
 Therefore, power directly depends on the crosssectional area of the filament. The crosssectional area corresponds to the thickness of the filament.
 The greater the power dissipated, the greater the thickness of the filament. Thus, 80 W filament is thicker.