Identical Batteries in Parallel do not Draw Same Current, Non-Ideal?

[BuddyBoy]

Homework Statement

Evaluate if identical batteries in parallel draw the same current when connected with a conductor with resistance.

Relevant Equations

V = IR

Theoretical thought experiment, trying to evaluate batteries in parallel, connected with non ideal conductors that have same current draw? Trying to understand the concepts here.

If I have three identical cells. Fully charged. Same age. Charged and discharged the same amount of times. Each cell has the same internal resistance $r_{int}$. Lets say they are connected to a load that draws $3 A$. I'm reading that each cell would draw the same current $1 A$. Something like below:

Is this true though if I consider the resistance in the conductor? Say the top and bottom conductor are two separate identical conductors. The top conductor is a single nickel strip with width $W$, thickness $t$ and length $L$. This single nickel strip is placed across the positive poles of the three cells and to the load. Something similar is done for the negative poles. Consider that the distance between the first cell and the second, as well as the second and the third, is the same displacement. But the length between the third cell and the load is some other length. Now I can calculate the total resistance of the top conductor easily.
$$R = \frac{\rho\;L}{Wt}$$

Is it possible to calculate the values of R1 R2 and R3? If say for example I know that the cells are 3.7 V? I'm seeing some problems with assuming that each cell draws 1/3 of the current or 1A, like below.

The voltage at Node Z must be
$$3.7\;V - (1\;A)(r_{int})$$
But wouldn't this also be the voltage at node Y? If the nodes are at the same voltage, than there is no current flow between nodes Z and Y. So I'm wondering how do I model this circuit, and what I'm doing wrong exactly?

It seems like the non-ideal resistance has to be placed right before and after the load.

But I'm not understanding why exactly. The nickel strip connecting the first and second cells has some none zero resistance between these two points.

 

[erobz]

When you include the conductor connecting the batteries the batteries are really not exactly in true parallel where node $Z$ and $Y$ are at the same potential. Think, if there is current flowing through $R_1$ there is a potential difference across $R_1$. How then can $Z$ and $Y$ be at the same potential?

 

[erobz]

In your lower picture $Z$,$Y$, and presumably$X$ are all at the same potential because you are assuming a conductor that joins them of zero resistance...in practice it just a very large conductor (negligible resistance) in comparison to other resistances in the circuit.

 

[BuddyBoy]

When you include the conductor connecting the batteries the batteries are really not exactly in true parallel where node $Z$ and $Y$ are at the same potential. Think, if there is current flowing through $R_1$ there is a potential difference across $R_1$. How then can $Z$ and $Y$ be at the same potential?

Thanks confirming. This is exactly what I was thinking.

Is there a way to calculate R1 R2 and R3? If you can estimate the length between the two points? I'm not sure if

$$R = \frac{\rho\;L}{Wt}$$

Can also be used if I don't consider the whole length, but only between two points on the conductor, not necessarily the end points?

 

[erobz]

Thanks confirming. This is exactly what I was thinking.

Is there a way to calculate R1 R2 and R3? If you can estimate the length between the two points? I'm not sure if

$$R = \frac{\rho\;L}{Wt}$$

Can also be used if I don't consider the whole length, but only between two points on the conductor, not necessarily the end points?

What do you mean? If you mean what are the $R$ values such that each battery contributes exactly 1 amp at the same voltage $V$... it's simply not real.

What you can say is you have made a connection of resistance $R$ between each battery and then calculate the amp contributions from each battery. Are you asking what is the resistance of the conductors that connects each of them so that this is reasonably the case? If so, then the onus is on you to decide what are reasonably acceptable deviations from "true parallel batteries-i.e. perfection". If you are not asking this, I don't follow.

Also, before I get in too deep (trying to be a hero), electrical networks/components, not my field... Not much is my field, but it's definitely not something I go out of my way to enjoy.

 

[DaveE]

This current sharing problem is well known in high current or low impedance circuits. In my case, a capacitor discharge network into a flashlamp (something like 1.2KA in 100-200usec, IIRC). The standard approach is to wire the load as shown below. Try to repeat your analysis with the conductor resistance in this configuration to see why we do this.

 

[pbuk]

The nickel strip connecting the first and second cells has some none zero resistance between these two points.

in practice it just a very large conductor (negligible resistance) in comparison to other resistances in the circuit.

This.

In this thread you spent 65 posts trying to design a nickel strip connector by calculating its heat loss. Do you see now why this was a waste of time?

We use nickel strips for connecting cells because they are (i) cheap and (ii) easily connected mechanically to the battery terminals by temporary (e.g. springs riveted through the strip) or permanent (e.g. spot welds) connections. In order to form these mechanical connections so that they operate reliably over the service life of the battery pack in the conditions it is designed for (vibration, mechanical shock etc.) the strip needs to be reasonably thick. (How thick? Do you think this is something you can calculate? If not, how do you think we can find out if the design meets this requirement?). For low current applications, any strip that is thick enough to meet the mechanical requirements will have negligible internal resistance.

For high current applications, resistance becomes non-negligible. Do you think we do some calculations to work out how much more nickel to use? What factors now become important in choosing a material for the connector? How can we reduce the current through the connectors while providing the same power?

If you want to start finding out about how high current battery packs are made the best use of your time would be to watch some videos like this one and to think about the questions I have asked:
.
Absolutely the worst use of everyone's time is to continue posting threads here about calculations on nickel strips.

 

[Steve4Physics]

Theoretical thought experiment, trying to evaluate batteries in parallel, connected with non ideal conductors that have same current draw? Trying to understand the concepts here.

To add to what's already been said, consider the simplest case of 2 batteries (or, more correctly, cells) in parallel.

Look at the following diagram (internal resistances omitted for simplicity).

'Connector resistance 1' is the total resistance of wires/strips connecting the left cell to the load.

'Connector resistance 2' is the total resistance of wires/strips connecting the right cell to the load.

Consider the symmetry. You should see:
a) If the connector resistances are equal, the currents through the cells are equal.
b) If the connector resistances are unequal, the currents through the cells are unequal.

I agree with @pbuk - forget about nickel strips!