Solving Car Battery Power Output Problem

[Prodigalvanic]

Homework Statement

A car battery with 12V EMF charged to 120amp hours. Assume potential difference across terminals is constant. How long can the battery deliver energy at a rate of 100Watts.
Missing is current (i), internat resistance (r), and real voltage (Vr)

Homework Equations

(Amp hours)*(real voltage)=(watt hours)
EMF-i*r=V
i*EMF-(i^2)*r=Watts
Watts=i*V

The Attempt at a Solution

There needs to be a way to eliminate any of the three variables i,r,Vr.
I think I am missing an equation.

(1)...i*(12V=EMF)-(i^2)r=100W reduces to -r=100W/(i^2)-12V/i
(2)...(12V=EMF)-i*r=I*Vr reduces to -r=(Vr-12V)/i
(3)... combine 1&2 to get (V-12)/i=100/(i^2)-12/i
That was pointless! There are still two variables but maybe you know something I don't.

I can assign arbitrary guesses to either r or i and then work it out and check if my resultant Vr is under 12V but that produces a range of possible answers. Namely any i and any r such that (i*r) is less than 12V and more than 0 will produce a possible Vr. Furthermore any unique possible Vr multiplied with 120amp hours results in a unique possible battery life.

There has to be another equation to derive the one I need!

 

[gneill]

Watts = I*V is a good place to start. If the battery is producing a constant 100W at 12V, what is the constant current?

 

[Prodigalvanic]

Watts = I*V is a good place to start. If the battery is producing a constant 100W at 12V, what is the constant current?

The V in "watts=i*V" is the real V (Vr) not the emf. The battery is not producing 100W at 12V its producing 100W and its emf is 12V.
To answer "what is the constant current?". Thats the missing value (i). I don't know where to go from here but I think its different equations.
There is a good problem solving technique called "its all about the joules". If i can relate joules available to use in the battery with joules used that should do it. But I don't know which equations to derive. I'll try to find suspects and share them.

 

[gneill]

According to the problem statement, "Assume potential difference across terminals is constant". That declares the voltage to remain at 12V, like it or not. This is a DC circuit, so one does not expect current versus voltage phase differences. The "real" V is 12V. The emf is 12V. They're one and the same here.

It could be that you're making your life harder by overthinking the problem.

 

[Prodigalvanic]

It could be that you're making your life harder by overthinking the problem.

It wouldn't be the first time. The definition of a "real" battery is that the potential across it's terminals is not equal to the emf. Thats why the question is worded with the key phrase "voltage across the terminals". The statement appears to declare that this voltage across the terminals is constant, if the battery were ideal that voltage would be 12V.
The problem statement uses two key phrases: A-"car battery" (none of which are ideal) B-"...voltage across the terminals is constant" (why use so many words rather than "...emf is constant" if not to drop a hint?)
That said, your disagreement is enough of a sanity check. I have class tomorrow, Ill ask then.

 

[Prodigalvanic]

Resolved, I was "overthinking it". Actually I thinks its an ambiguous question but that's normal for textbooks.