# Which of the following statements is TRUE if the filaments of 40 W and 80 W bulbs are of the same length?

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Which of the following statements is TRUE if the filaments of 40 W and 80 W bulbs are of the same length?
1. 80 W filament is thicker
2. 40 W filament is thicker
3. Both cannot have the same length
4. Both are of same thickness

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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 cross-sectional 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 cross-section.

• 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 cross-sectional area of the filament. The cross-sectional 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.