Can Two Batteries Simultaneously Act as Both the Source and Load in a Circuit?

[Evil Bunny]

Probably a very simple question, but I'm not sure of the answer...

We have two batteries.

Scenario 1: The positive terminals of both batteries are connected together and the negative terminals are connected together. Little to no current flows, correct?

Scenario 2:
The positive terminal of battery A is connected to the negative terminal of battery B.
The positive terminal of battery B is connected to the negative terminal of battery A.
Now we have lots of current flowing, correct?

In scenario 1, apparently no circuit was completed, yet in scenario 2 we must have completed a circuit... Why? Did both batteries (of scenario 2) simultaneously become the sources and the loads? How would you calculate the current flow?

 

[tiny-tim]

Hi Evil Bunny!

In scenario 1, apparently no circuit was completed, yet in scenario 2 we must have completed a circuit... Why? Did both batteries (of scenario 2) simultaneously become the sources and the loads? How would you calculate the current flow?

This is exactly what happens if you connect two 1.5 V batteries together the "correct" way, and then complete the circuit with only a wire …

the total voltage will be 3 V, and if the total internal resistance (plus the negligible resistance of the wire) is R Ω, then the current will be 3/R A, and the power drain (although you can't see it) will be 9/R W.

 

[shoestring]

In scenario 1, apparently no circuit was completed, yet in scenario 2 we must have completed a circuit... Why? Did both batteries (of scenario 2) simultaneously become the sources and the loads? How would you calculate the current flow?

This makes me wonder exactly what we mean by the word "circuit". We certainly have a loop of some kind in scenario 1, but no current. (A simple metal ring with no battery is a loop, but without a current, unless there's a time-varying magnetic flux through the loop, of course.)

Scenario 1 has two batteries in parallel, so that "loop" is in itself a voltage source, having the same voltage as a single battery, like in this picture. But, should we call that a "circuit"? An open circuit perhaps? (Image from http://itp.nyu.edu/physcomp/Notes/Batteries")

[PLAIN]http://itp.nyu.edu/physcomp/uploads/battery_parallel.jpg

 

[Evil Bunny]

I guess not... it's only a circuit if the negative side makes it's way back to the positive side. And apparently the source becomes it's own (very low resistance) load when we short the two terminals. Interesting...

 

[nasu]

It is a circuit (loop) no matter which way you connect them. The resistance of the circuit is 2r where r is the internal resistance of the battery. The sum of the emfs is E-E in the first case and E+E in the second case. (see Kirchoff's second law, for example).
So in the first case
I*2r= 0 and I=0
and in the second case
I*2r= 2E so I= E/r.
These cases bot refer to a circuit with just batteries. No external load.