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

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To calculate the filament area ratio between a main lamp and a car headlamp, one must first determine the current for each lamp using the formula W = I²R. Given the mains lamp operates at 230V and 100W, and the car headlamp at 12V and 36W, the current can be calculated as follows: for the mains lamp, I = √(W/R) and for the car headlamp, I = √(W/R). The difference in current between the two lamps will affect the resistance and, consequently, the cross-sectional area of the filaments. Understanding these relationships is crucial for calculating the desired ratio of cross-sectional areas.
marco123
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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
 
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marco123 said:
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?
 

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