Question

For a three-way bulb (55 W, 80 W, 135 W) that is designed to operate at 110 V, find the resistance of each of the two filaments. Assume that the wattage ratings are not limited by significant figures, and ignore any heating effects on the resistances.

Answer 1

(1) 55W bulb has 220 ohms.

(2) 80W bulb has 150.25ohms.

(3) 135W bulb has 89.63ohms.

Step-by-step explanation:

Power is related to voltage and resistance by.

`P = (V^2)/(R)`

modifying this formula for R gives.

`R = (V^2)/(P)`

we have fixed voltage for all three bulbs and powers are given, so we can use modified equation to calculate resistance.

(1) 55W

`R = (V^2)/(P) = ((110V)^2)/(55W) =220ohms.`

(2) 80W

`R = (V^2)/(P)=((110V)^2)/(80W)=151.25ohms.`

(3) 135W

`R = (V^2)/(P) = ((110v)^2)/(135W) =89.63ohms.`