Efficiency - how to get the maximum efficiency in a circuit?

[alexmath]

efficiency -- how to get the maximum efficiency in a circuit?

Homework Statement

I don't quite understand how to get the maximum efficiency in a circuit.

Exemple.

4 Volts and 2.0Ω will produce 8 watts with a current of 2.0 amps.
5 Volts and 3.1Ω will produce 8 watts with a current of 1.6 amps.

There are infinitely ways to do so. Also we have an led which has to be connected.

Homework Equations

P=UI=I^2*R=U^2/R

The Attempt at a Solution

My intuition says that the first one is more efficient, but the battery will drain faster. I really want to know how to mix this information together for my circuit.

 

[BvU]

Hello Lex,
What is the question ? How to most efficiently do what exactly ?

 

[CWatters]

More details are required.

4 Volts and 2.0Ω will produce 8 watts with a current of 2.0 amps.
5 Volts and 3.1Ω will produce 8 watts with a current of 1.6 amps.

Both are 100% efficient if the wanted output is heat.

Both are 0% efficient if the wanted output is light (because there is no light bulb or LED in the circuit as described so far).