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

Answer:

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

Explanation:

The equation for electric power is

power P = IV

also,  I = V/R,

substituting into the equation, we have

$P = \frac{V^{2} }{R}$

$R = \frac{V^{2} }{P}$

a)  $R = \frac{1.5^{2} }{0.8}$ = 2.8 Ω

b) $R = \frac{3^{2} }{6}$ = 1.5 Ω

c) $R = \frac{4.5^{2} }{4}$ 5.06 Ω

d) $R = \frac{6^{2} }{8}$ = 4.5 Ω

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

C. 4 W, 4.5 V