Question

Lightbulbs are typically rated by their power dissipation when operated at a given voltage. Which of the following lightbulbs has the largest resistance when operated at the voltage for which it's rated?

A. 0.8 W, 1.5 V
B. 6 W 3 V
C. 4 W, 4.5 V
D. 8 W, 6 V

Answer 1

The arrangement with the greatest resistance is the light bulb of option C. 4 W, 4.5 V

Step-by-step explanation:

The equation for electric power is

power P = IV

also, I = V/R,

substituting into the equation, we have

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

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

a)
`R = (1.5^(2) )/(0.8)` = 2.8 Ω

b)
`R = (3^(2) )/(6)` = 1.5 Ω

c)
`R = (4.5^(2) )/(4)` 5.06 Ω

d)
`R = (6^(2) )/(8)` = 4.5 Ω

from the calculations, one can see that the lightbulb with te greates resistance is

C. 4 W, 4.5 V