Question

A 50-watt lightbulb and a 100-watt lightbulb are each operated at 110 volts. Compared to the resis- tance of the 50-watt bulb, the resistance of the 100- watt bulb is

Answer 1

(1) 50 watt bulb has 242 Ohms of resistance.

(2) 100 watt bulb has 121 Ohms of resistance.

Step-by-step explanation:

p = IV

Case (1) 50 watt bulb.

50w = I(110v), I = 0.454545Amperes.

from ohms law.

V = IR

solving for R gives, R = 110V/0.454545A = 242Ohms.

Case(2) 100 watt bulb.

100w = I(110v), I = 0.909090Amperes.

and similarly from ohms law.

R = 110V/0.909090A = 121Ohms.

Answer 2

R = 242Ω

R = 121Ω

Step-by-step explanation:

To find the resistance of both light-bulbs you can use the formula:

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

V: potential of the bulbs - 110V

R: resistance of the light bulbs

P: power (50W - 100W)

By replacing you obtain:

for P=50W

`R=((110V)^2)/(50W)=242\Omega`

for P=100W

`R=((110V)^2)/(100W)=121\Omega`

hence, the resistance of the light bulb with 100W is one half of the light bulb of 50W