How Do You Calculate the Filament Area Ratio Between Main and Car Head Lamps?

[marco123]

hi all i have a question to do but i can't seem to get my head round it and i was hoping some of you might be able to explain it better so here it is:
"the coiled filaments in a main lamp and a car head lamp are made of the same material and have the same length. Use the info. below to calculate the ratio:
cross sectional area of the mains lamp filament/cross sectional area of the headlamp filament

Mains lamp: 230V; 100W Car headlamp;12V; 36W

Many thanks
Marco

 

[LowlyPion]

hi all i have a question to do but i can't seem to get my head round it and i was hoping some of you might be able to explain it better so here it is:
"the coiled filaments in a main lamp and a car head lamp are made of the same material and have the same length. Use the info. below to calculate the ratio:
cross sectional area of the mains lamp filament/cross sectional area of the headlamp filament

Mains lamp: 230V; 100W Car headlamp;12V; 36W

Many thanks
Marco

Your power is W = I²R

What do you suppose are the differences in current between the 2?

 

[baba89]

Hello Marco,

The ratio of the cross sectional area of the mains lamp filament to the cross sectional area of the car headlamp filament can be calculated using the formula:

(Area of mains lamp filament)/(Area of car headlamp filament) = (Voltage of mains lamp)^2 x (Power of car headlamp)/ (Voltage of car headlamp)^2 x (Power of mains lamp)

Substituting the given values, we get:

(Area of mains lamp filament)/(Area of car headlamp filament) = (230V)^2 x (36W)/ (12V)^2 x (100W)

= 529 x 36/144 x 100

= 19044/14400

= 1.32

Therefore, the ratio of the cross sectional area of the mains lamp filament to the cross sectional area of the car headlamp filament is approximately 1.32. This means that the mains lamp filament is about 1.32 times thicker than the car headlamp filament.

I hope this helps to clarify the question for you. Remember to always use the appropriate formulas and units when solving scientific problems. If you have any further questions, feel free to ask. Good luck!