Question

Bulb ܣ is rated for 20W at 12V. Bulb ܤ is rated for 20W at 120V. The two bulbs are mistakenly mixed up so that bulb ܣ is connected to a 120V line and bulb ܤ is connected to a 12V line. a. Determine the power dissipated by Bulb ܣ while connected to the 120Vline. b. Determine the power dissipated by Bulb ܤ while connected to the 12Vline. c. Which bulb, if any, is more likely to burn out and why?

Answer 1

Answer:

a. 2000W

b.0.2W

c. Bulb 1

Explanation:

Data given:

bulb 1 rating =20w,12v

bulb 2 rating =20w,120v.

we calculate the resistance for each bulb

$bulb 1: R=\frac{V^2}{P}\\ bulb 1: R=\frac{12^2}{20}\\ R=7.2 ohms$

for bulb 2

$bulb 2: R=\frac{V^2}{P}\\ bulb 2: R=\frac{120^2}{20}\\ R=720 ohms$

when miss connection occur we need to calculate the dissipated power from wash bulb

a. for bulb 1 with R=7.2ohms and V=120v,

the power is calculated as

$P=\frac{v^2}{R}\\ P=\frac{120^2}{7.2}\\ P=2000W$

b. for bulb 2 with R=720 ohms and V=12v,

the power is calculated as

$P=\frac{v^2}{R}\\ P=\frac{12^2}{720}\\ P=0.2W$

c. Bulb 1 is more likely to burn out because it is operating above the rated power.