Batteries in series

[Boricua27]

Good luck to those of you that will take the MCAT soon. I take it on Wednesday. Here's a last minute question. I would appreciate if someone shared their insight. It's from The Princeton Review Hyperlearning Science Workbook, General Chemistry Passage 86, #2.

First, I'll share the passage's references to current:

"Although there is a standard voltage defined for a given electrochemical cell, there is no standard current. The current produced by a cell is directly proportional to the surface area of the cathode and the anode; it is completely independent of the chemical nature of the cell. Therefore, regardless of a cell's voltage, the larger an electrochemical cell, the larger the output current.

Electrochemical cell that are wired in series produce an electron flow in which the currents (denoted by I) are the same in them all, and with a new voltage (V) which is the sum of these cells:
I(subscript: a) = I(b) = I(c)
V(sub: total) = V (cell A) + V (cell B) + V (cell C)

In a similar fashion, the current of an electron flow may be increased. The amperage of a single cell may be enhanced by increasing the surface area of the internal electrodes.

[Reduction potential of F2: +2.87]
[Reduction potential of Zn2+: -0.76]"​

...OK! The question: "The current of three zinc-fluorine batteries wired in series is: ..." I thought: OK, the formula for current is in the passage, and it says, "cells that are wired in series produce an electron flow in which the currents are the same in them all." So if I(a) = I(b) = I(c) in series, then the current of three batteries in series equals the current of a single battery. Apparently, the answer is "indeterminate based upon this information." The book explains its interpretation: "The current of a number of identical cells wired in series is always equal to the current of one of the separate cells. However this choice does not appear here... Choice C ("equal to that produced by a single Zn-F battery) is an incorrect statement; a cell's voltage cannot be used to predict the current. In order to determine the I(total), you must be provided with the current of a single cell, or at the very least, more information that can be used to determine I(cell)."



I predicted choice C: "equal to that produced by a single Zn-F battery." The voltage (based on reduction potentials) is provided, and I(cell) can be determined if more information -- R(cell), I think -- is provided, but it is not. I get that. But I think that the passage (and background knowledge, even) provided enough information to express the total current of the three-battery series circuit. I do not need to use values for voltage or resistance since one of the answer choices provides an answer that is not numerical, but instead a relationship. Although I cannot figure out the numerical value of I(cell), I know that I(cell) = I(cell 2) = I(cell 3) = I(total). If one of the batteries in series produces a certain current, then the other batteries, and the entire three-battery series, must produce the same current--even if I can't assign it a numerical value unknown (as is the case).

To illustrate my thinking, let's pretend that the resistance of a single battery (R(cell)) is 0.1 ohm.
I will use Ohm's law (V=IR) and the equation "Voltage = E(cell) = E(red) + E(ox)."

E(cell) = EMF = E(red) + E(ox) = 2.87 + 0.76 = 3.63 Volts
R(cell) = 0.1 ohm

V(cell) = I(cell)R(cell)
3.63 Volts = I(cell) * 0.1 ohm
... I(cell) = 3.63 Volts / 0.1 ohm
I(cell) = ~ 36 amperes
​

Since I(cell) is the current produced by a battery in series, then I(cell) = I(cell2) = I(cell3) = I(total).
Therefore, I(cell) = 36 amperes = I(total)
​

In the question, I can't assign I(cell) a number, but I can still say:

I(cell) = X ; where "X" is a variable​

I can, then, say:

I(cell) = I(cell2) = I(cell3) = I(total)
So I(total) = X​

If I consider the question like that, then it seems like my original answer choice ("[I(total)] is equal to [the current] produced by a single Zn-F battery") is correct!

I hope that someone with a better understanding of circuits than me will clarify this.

Thanks,
Bryan

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[gettheleadout]

Moving to Q&A.

 

[milski]

You need to know both the internal resistance (the 0.1 ohm that you are using) and the resistance of the load to which the battery is connected. If you assume that it stays the same between the one battery and the three battery cases, the currents will certainly be different. And if it changes, it has to change in a very specific way for the current to stays the same. The question does not say anything about what happens to the load, so you cannot say anything about the current. It is still worded in a confusing way - not something I have seen in AMCAS material.

 

[Boricua27]

You need to know both the internal resistance (the 0.1 ohm that you are using) and the resistance of the load to which the battery is connected. If you assume that it stays the same between the one battery and the three battery cases, the currents will certainly be different. And if it changes, it has to change in a very specific way for the current to stays the same. The question does not say anything about what happens to the load, so you cannot say anything about the current. It is still worded in a confusing way - not something I have seen in AMCAS material.

Thanks for replying, Milski. I think I understand what you mean.

"The current of a number of identical cells wired in series is always equal to the current of one of the separate cells."

That wrong answer refers to "one of the separate cells," so the current it refers to is produced based on the voltage and that specific battery's resistance. Then, once that battery is hooked up to two other batteries, it will not produce the same current because the R(total) is different from R(cell1). It also sounds like the three batteries in series will reach electrical equilibrium, where V(cell1) = V(total), R(total) = R(cell1) + R(cell2) + R(cell3), and I(total) depends on R(total).

Is this right?

I(cell1, separate) = X (or .1 ohms, for example)

I(cell1, separate) =/= I(cell1, series)​

I(cell1, series) = I(cell2, series) = V(total) / R(total)

Then R(total) is missing because R(cell1), R(cell2), and R(cell3) are missing.
​

I think I may still be missing something. You mentioned internal resistance of the batteries and the resistance of the load. Is the sum of those two values called R(total)? I think R(cell1) is the internal resistance of battery 1. Then should R(total) also include a value for "resistance of the load," like you mentioned?

 

[milski]

I'm not perfectly clear what point exactly they are trying to make with this question. You are correct that R_total=R₁+R₂+R₃. Since the batteries are in series, the same is true for the voltage, V_total=V₁+V₂+V₃

Unless you know that R₁=R₂=R₃, you cannot claim that I_total is the same as either of I_1,2,3.

But they are not even telling you that when the three batteries are connected, the corresponding resistance are kept as part of the circuit, so you cannot claim much at all.

I think they might be trying to say that while the battery will have the same voltage regardless of how it's connected in a circuit, it will have different currents going through it in different circuits?

You can ignore my comments about internal resistance - I mentioned it because you were talking about 'resistance of a battery' but I don't think that's what you meant.