Maximum power from a battery with source resistance

[JordanHood]

Homework Statement

A 5V battery rated at 1800mAh has a soucre resistance of 10 Ohms. What is the maximum power that can be extracted from the battery?

Homework Equations

The Attempt at a Solution

I understand that had the battery not had any source resistance then the power out would have been equal to Energy x Time giving us P=VIT, but i do no understand what to do when there is a source resistance. Do I calculate another current that is passing through the battery? using V=IR to get a current of 0.5A? If so then what does the 1800mAh mean? I have then tried putting this current into P=I^2R but this means I am totally ignoring one of the values in the question which means I can't be right

EDIT
Apologies I didnt realize this was a multiple choice question, the possible answers are
a) 625mW
b) 1.25mW
c) 2.5 mJ
d) 11.664 MJ

 

[cnh1995]

Homework Statement

A 5V battery rated at 1800mAh has a soucre resistance of 10 Ohms. What is the maximum power that can be extracted from the battery?

Homework Equations

The Attempt at a Solution

I understand that had the battery not had any source resistance then the power out would have been equal to Energy x Time giving us P=VIT, but i do no understand what to do when there is a source resistance. Do I calculate another current that is passing through the battery? using V=IR to get a current of 0.5A? If so then what does the 1800mAh mean? I have then tried putting this current into P=I^2R but this means I am totally ignoring one of the values in the question which means I can't be right

I don't see the significance of 1800mAh in this problem. Do you know the maximum power transfer theorem in electrical circuits?

 

[JordanHood]

I don't see the significance of 1800mAh in this problem. Do you know the maximum power transfer theorem in electrical circuits?

Is this when the source resistance and load resistance are equal?

 

[cnh1995]

Is this when the source resistance and load resistance are equal?

Yes. But I just realized that the theorem will give the value of load resistance for maximum power dissipation in the load, while the question asks about the maximum power in the entire circuit.

 

[cnh1995]

I believe 1800mAh means the battery can supply 1800mA current for 1hr.
Edit: I think the proper meaning of this is that the battery can supply 1mA current for 1800 hrs.

 

[JordanHood]

I believe 1800mAh means the battery can supply 1800mA current for 1hr.

So do I need to calculate the current per second?

 

[cnh1995]

So do I need to calculate the current per second?

No. Seeing the options, I think this problem does belong to the maximum power transfer theorem. After all, it's the load that extracts power from the battery. So when we say 'power extracted from the battery', it means the power consumed by the load from the battery.

 

[JordanHood]

No. Seeing the options, I think this problem does belong to the maximum power transfer theorem. After all, it's the load that extracts power from the battery. So when we say 'power extracted from the battery', it means the power consumed by the load from the battery.

Ok so I set the internal resistance of the battery to 10 Ohms and work from there?

 

[cnh1995]

Ok so I set the internal resistance of the battery to 10 Ohms and work from there?

I think so.

 

[JordanHood]

I think so.

That gives me 625mW, which is one of the answers, so assuming that is right. Bit concerned about not using the 1800mAh at all though, possibly there to confuse you?

 

[NascentOxygen]

power out would have been equal to Energy x Time giving us P=VIT, but i do no understand

No. Energy delivered = power x time

But you are not asked about energy, the question involves maximizing output power.

 

[cnh1995]

Bit concerned about not using the 1800mAh at all though, possibly there to confuse you?

I think so. I haven't seen mAh rating being used for calculating maximum power so far.