Question

A string of 18 identical holiday tree lights is connected inseries to a 190V source. The string dissipates 62.0 W. One of thebulbs burns out. The lamp has a wire that shorts out the lampfilament when it burns out. This drops the resistance of the lampto zero.(a) What is the resistance of the light string now?(b) Find the power dissipated by the string.(c) Did the power go up or down when a bulb burned out?

Answer 1

549.9 ohms, 65.65 watts, the power went up

Explanation: power P = V²/R

v= 190volts , P =62watts

from P =V²/R

62=190²/R

making R the subject

R×62= 190²

62R =36100

R=36100/62

R=586.25 ohms

Resistance of each lamp = 586.26/18 =32.3ohms

a) resistance of the light string now = 17×32.3 = 549.9 ohms

b) P=V²/R

where R=549.9ohms , P=?

P=190²/549.9

P=36100/549.9

P=65.65watts

Power dissipated has increased( went up )