# Question Video: Understanding The Potential Difference across The Two Terminals of a Cell Science

A cell does work on the charges within it to create a separation of charge across its two terminals. Complete the following sentence: The potential difference provided by the cell is equal to the ＿ divided by the ＿. [A] amount of charge that has been separated, amount of work done [B] amount of charge that has been separated, distance between the terminals [C] amount of work done, amount of charge that has been separated [D] amount of work done, distance between the terminals

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### Video Transcript

A cell does work on the charges within it to create a separation of charge across its two terminals. Complete the following sentence: The potential difference provided by the cell is equal to the blank divided by the blank. (A) Amount of charge that has been separated, amount of work done. (B) Amount of charge that has been separated, distance between the terminals. (C) Amount of work done, amount of charge that has been separated. (D) Amount of work done, distance between the terminals.

Knowing that we’re working here with a cell, let’s clear some space at the top of our screen and consider what’s happening in this cell. This cell contains electric charges. It has positive charges, we’ve shown them here in red, arranged in an orderly grid. And it also has negative charges here in blue. These charges are able to move throughout the cell. We’re told that the cell does work on these charges to separate them. This means it exerts forces on the charges and causes them to move. We mentioned that the red charges, the positive ones, are fixed in place, but the blue negative charges can move. So this force will make the blue negative charges concentrate at one end of the cell.

For that reason, this end of the cell is called its negative terminal. And that means the other end, where there are more positive than negative charges, is the positive terminal. So the cell has done work on the charges within it to create a charge separation. This separation of charges means there’s now a potential difference across the cell.

We want to know which of our four answer options best describes this potential difference by filling in the gaps in our sentence. The first thing we can say about this potential difference is that it depends on the amount of work that was done to separate the charges in the cell. The greater the amount of work, the more negative charges would tend toward the negative terminal, and therefore the larger the potential difference would be. Now, notice that our sentence is describing a fraction. Whatever goes in the first blank is being divided by whatever goes in the second blank. We can think of this sentence in fact as being similar to a mathematical equation for potential difference.

Clearing just a bit more space still, we can write that that equation would go like this. The potential difference provided by the cell, we’ll call it PD, is equal to whatever goes in the first blank of our sentence divided by whatever goes in the second blank. A moment ago, we noted that the more work was done on the charges in the cell, the greater the potential difference across the cell would be. And that tells us what must go in the first blank in our sentence. The amount of work done by the cell must be in the numerator of this fraction. Looking over our answer options, we see that only options (C) and (D) have the amount of work done going in that first blank.

Right away then, we can eliminate options (A) and (B) from consideration. Options (C) and (D) are different in what they suggest for completing the second blank. Choice (C) gives the amount of charge that has been separated. Option (D), on the other hand, describes the distance between the terminals, that is, the physical distance between the positive and negative terminals of our cell.

Now, let’s think for a moment about work as it applies in physical situations. The work done on an object, say, one of these charges in the cell, is equal to the force exerted on that charge multiplied by the distance the charge travels. In other words, the distance these charges move is already included in this idea of work. We don’t need to take that distance into account again, as option (D) suggests. If, instead of distance, we put charge in the denominator of this fraction, then we see that for some fixed amount of work done on the charges, more charge having to be separated means that fixed amount of work doesn’t separate the charge very much. And that means that the potential difference is not so great.

On the other hand, for a smaller amount of charge, a fixed amount of work can push those charges relatively farther apart from one another. Fewer charges to separate then means a greater potential difference again for a given amount of work done. It does make sense then that work would go in the numerator of this fraction and charge in the denominator. For our answer then, we choose option (C). The potential difference provided by the cell is equal to the amount of work done divided by the amount of charge that has been separated.