PD across the terminals of two cells

[moenste]

Okay, so discharging means current is flowing out of the + terminals of the battery, charging means current is flowing into the + terminal of the battery. Now you have to ponder how to maximize each of those with the given circuit. Remember, the only thing you can adjust is the position of the tap F on the potentiometer.

I think it all goes to the fact we need to put 10 Ω into one side. Like F should be placed either at G or at E.

If we put F at E:
10 - 10 I₁ + 10 I₃ - 2 I₁ = 0
-3 - 3 I₃ + 10 I₁ - 10 I₃ = 0
So I₃, flowing through B is 1.15 A.

If we put F at G:
10 - 12 I₁ = 0
I₁ = 0.83 A

-3 - 3 I₃ = 0
So I₃ = 1 A.

And so then we need to put F at E to make cell B charge at the maximum possible rate and put F at G to discharge B at maximum possible rate.

 

[gneill]

I agree with your reasoning as to where to place the potentiometer tap for maximizing charging or discharging.

 

[moenste]

I agree with your reasoning as to where to place the potentiometer tap for maximizing charging or discharging.

So it's correct? I was unsure about putting at G. And the calculations (at least the logic) are correct?

And in general: higher current flow is charging (better for charge), lower current flow is discharging (better for discharge)?

 

[gneill]

So it's correct? I was unsure about putting at G. And the calculations (at least the logic) are correct?

It looks okay. I calculate a slightly lower value for the charging current (1.14 A), but that could simply be a matter of rounding (I round down from 1.142 A).

And in general: higher current flow is charging (better for charge), lower current flow is discharging (better for discharge)?

Well, most people like their batteries to charge quickly but last a long time, so in that sense it's better. In real life one has to be careful about charging or discharging too quickly to prevent damaging the cell.

 

[gneill]

If you write your loop equations making the portion of the potentiometer shared by both loops a variable Rx (where Rx would range from 0 to 10 Ohms), then you can find a single equation for the B cell current that depends on the value of Rx, or equivalently, the position of the slider. With that you can plot a curve of the current versus position. Here's one that I just did, prettied up a bit to describe what's happening: