Two light bulbs designed for 120-V use are rated at 40W and 60W. Which light bulb has the greater filament resistance? Why? Answer (2400 Ω, 3600 Î©) 



Given:

Voltage =  V = 120 V

Power of 1st light Bulb = P₁ = 40 W

Power of 2nd light Bulb = P₂ = 60 W

To Find:

Resistance of filament of 40 W light Bulb = R₁ = ?

Resistance of filament of 60 W light Bulb = R₂ = ?

Which light bulb has greater filament resistance? and Why? 

Solution:


The general formula of Resistance R in term of Voltage V and Power P is 

R = `\frac {V^2}{P}` --------------(1)


Filament resistance R₁ of the light bulb of 40 W:

R₁ = `\frac {V^2}{P₁}`

putting values

R₁ = `\frac {(120 V)^2}{40 W}`

R₁ = `\frac {14400 V^2}{40 W}`

R₁ = 3600 Ω ---------------------(1)


Now to find the Filament resistance R₂ of a light bulb of 60 W:

R₂ = `\frac {V^2}{P₂}`

putting values

R₂ = `\frac {(120 V)^2}{60 W}`

R₂ = `\frac {14400 V^2}{60 W}`

R₂ = 2400 Ω ---------------------(2)

Equation No. (2) and (3) show that the filament resistance of a 40 W light bulb is greater than the filament of a 60 W light bulb. 

The resistance of a light bulb filament depends upon both on the length and cross-sectional area of the filament wire. Thinner wire ( having a low cross-sectional area) has greater resistance and a small amount will be allowed to flow.

By assuming the lengths of filaments of both light bulbs are same. The 40 Watt bulb will have a thinner filament, greater resistance, and a smaller current than the 60-Watt bulb of thicker filament, less resistance, and greater current.


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