Calculating Engine Power for Headlights: Solving for Efficiency and Resistance

[4eleven]

The headlights of a certain moving car require 11 A from the 12 V alternator, which is driven by the engine. Assume the alternator is 84% efficient (its output electrical power is 84% of its input mechanical power), and calculate the power (in hp) the engine must supply to run the lights.

I plugged the equation into P = iV and multiplied it by .84 efficiency, then got my answer in watts, which I converted to hp. When I checked in my book, however, the answer was not correct. I'm pretty much stumped on how else to approach it.

 

[G01]

The headlights of a certain moving car require 11 A from the 12 V alternator, which is driven by the engine. Assume the alternator is 84% efficient (its output electrical power is 84% of its input mechanical power), and calculate the power (in hp) the engine must supply to run the lights.

I plugged the equation into P = iV and multiplied it by .84 efficiency, then got my answer in watts, which I converted to hp. When I checked in my book, however, the answer was not correct. I'm pretty much stumped on how else to approach it.

You should be dividing by .84, not multiplying by it:

$$P_{out}=.84P_{in}$$

Therefore,

$$P_{in}=\frac{P_{out}}{.84}=\frac{iV}{.84}$$

See where you went wrong?

Next time, please post homework type questions in the appropriate homework help forum.

 

[4eleven]

Ah! Yes! Thank you so much!

 

[G01]

Anytime.