What is power consumed by each bulb in 110V line ?

Question

Two electric bulbs,each designed to operate with the power of 500W in 220V line, are connected in series with 110V line.What is power consumed by each bulb ?

Answer 1

The first thing we should do is figure out the resistance of the bulbs in their normal operating situation. The relevant equation is

 

P = IV

 

Solving for the resistance isn't an obvious step here. Let's use Ohm's law to substitute what we want.

 

V = IR

 

I = V/R

 

Plugging that in yields

 

P = V²/R

 

Solving for R here gets

 

R = V²/P

 

Now we can figure out the resistance of the light bulbs.

 

R = 220²/500 = 96.8 Ohms (for each bulb)

 

The problem states that these bulbs are wired in series, so we simply add their resistances for a total of 193.6 ohms.

 

Now we use the Power equation we found earlier and plug in our new numbers.

 

P = V² / R = 100² / 193.6 = 62.5 Watts. This is the total power consumed by both bulbs. Since both bulbs have the same resistance, each consumes half of that power, or 31.25 Watts.

 

I hope this helps!