Circuit with potential difference across battery being zero?

[zenterix]

Homework Statement

Can one construct a circuit such that the potential difference across the terminals of a battery is zero?

Relevant Equations

The first circuit I thought about was something like the following

Using KVL we have $\epsilon_1-\epsilon_2+iR=0$.

It seems that $\epsilon_1,\epsilon_2$, and $R$ are given and the only variable is $i$.

Thus, $i=\frac{\epsilon_2-\epsilon_1}{R}$ for the KVL equation to be true.

However, it seems like when we think about what happens to this circuit in time, $\epsilon_1$ seems to be a variable as well.

Suppose $\epsilon_2>\epsilon_1$. Then current flows counterclockwise. It seems that this current would undo the chemical reactions inside of battery 1 and reduce its electromotive force.

The more $\epsilon_1$ decreases, the higher the current. Does this mean the reduction of $\epsilon_1$ speeds up as the process occurs?

How long would this happen for?

I imagine that zero is the lowest that $\epsilon_1$ can go, since when this happens battery 1 is acting like a short and $i=\frac{\epsilon_2}{R}$.

Actually, the first circuit I thought of didn't have the resistor $R$ in it.

$R$ can be thought of as an internal resistance of battery 1.

If this resistance were not there (and I guess this is not a realistic scenario), then my guess is that the emf of battery 1 would go to zero instantly and the flow of current would be, well, infinity.

But the resistance is there, and after $\epsilon_1$ goes to zero, $R$ represents the resistance of the current flowing through that battery. There is, however, a difference of potential across the resistor.

Since we are thinking of this resistance as actually being part of the battery, then it seems that what happens is that in the end, the difference of potential across battery 1 (including the resistance) actually stays the same at $\epsilon_2$, but now the entire potential difference is across the resistor.

I'm not sure what to make of this last statement yet.

 

[hutchphd]

As I think you understand, the circuit will require a very stout coppr bar and a "perfact" battery would supply very large current. As you rightly suspect this will be limited by the reaction rates in the battery (modeled as an interrnal resistance of the battery)

 

[kuruman]

As you rightly suspect this will be limited by the reaction rates in the battery (modeled as an interrnal resistance of the battery)

Would that not be a resistance inside the battery, not a short, which means non-zero potential difference across the battery terminals?

 

[willem2]

Homework Statement: Can one construct a circuit such that the potential difference across the terminals of a battery is zero?
Relevant Equations: The first circuit I thought about was something like the following

Suppose ϵ2>ϵ1. Then current flows counterclockwise. It seems that this current would undo the chemical reactions inside of battery 1 and reduce its electromotive force.

I don't know why you think this will happen? This depends on the exact battery chemistry, but at least with rechargeable batteries, this will charge the battery with the lower electromotive force, and it will raise its emf until the emfs of the batteries are the same. If R is large enough, this won't set anything on fire.