Question Video: Electromotive Force and Internal Resistance

Which of the following statements is a correct description of the electromotive force (emf) of a battery? [A] The emf of a battery is the voltage that it applies across a circuit to which it is connected. [B] The emf of a battery is the voltage required to overcome its internal resistance. [C] The emf of a battery is the current within the battery. [D] The emf of a battery is the potential difference across its terminals when it is not producing any current.

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Video Transcript

Which of the following statements is a correct description of the electromotive force, emf, of a battery? (A) The emf of a battery is the voltage that it applies across a circuit to which it is connected. (B) The emf of a battery is the voltage required to overcome its internal resistance. (C) The emf of a battery is the current within the battery. And (D) the emf of a battery is the potential difference across its terminals when it is not producing any current.

Okay, as we get started figuring out which of these four options is the correct description of the electromotive force or emf of a battery, let’s clear some space at the top of our screen. Now, when we talk about a battery, sometimes that term refers to a single unit, or a single cell like this, or other times it can refer to multiple cells strung end to end. For simplicity’s sake, we’ll refer to this single unit as a battery. And we want to identify a correct description of the emf of this battery. A battery, we can recall, is a device that converts chemical energy into electrical energy. It does this by chemically separating out electric charges, sending negative charges towards one end of the battery called the negative terminal. And that leaves an abundance of positive charges at the other terminal.

We can see that this battery, as is, is not part of an electric circuit. That means that there’s no charge flowing through the battery. Under these conditions, if we were to measure the electric potential at the positive end of the battery, the positive terminal, and also make a measurement of electric potential at the negative terminal. We could call the potential at the positive terminal 𝑉 sub plus and the potential at the negative terminal 𝑉 sub minus. Then, the emf of our battery is equal to the magnitude of the difference between these two potentials. In other words, emf is a potential difference. Looking through our answer options, we see that this matches up with option (D). But let’s look through the other answer options to see why it is that they’re incorrect.

Option (A) says that the emf of a battery is the voltage that it applies across a circuit to which it is connected. So, getting back to our battery, say that we connect it up so that it’s now part of an electrical circuit like this. Option (A) is saying that the battery’s emf is the voltage that it applies across the circuit to which it’s connected. In other words, it’s the potential difference created by the battery across this external part of the circuit, we could call it. The problem with this definition is it ignores the fact that the battery itself may have internal resistance. We often represent this internal resistance with a lowercase 𝑟. And this internal resistance, combined with the current inside the battery, diminishes the emf so that the voltage the battery applies across the rest of the circuit is actually less than the emf.

If the current in this circuit is equal to capital 𝐼, then that current multiplied by the internal resistance 𝑟 must be added to a voltage that we typically call 𝑉 in order to add up to the emf created by the battery. Answer option (A) describes a voltage that is applied across the rest of the circuit to which a battery is connected. That voltage is represented by this capital 𝑉 here. And we can see that that’s different from the emf. The only way that 𝑉 would equal emf is if the internal resistance of our battery were zero. Practically speaking though, this isn’t the case. And this is why answer option (A) won’t be our choice.

Moving on to answer option (B), this says that the emf of a battery is the voltage required to overcome its internal resistance. Well, it’s true that emf is a voltage, which may be surprising considering its name is a force. But looking back at our equation for emf, we could say that the voltage required to overcome a battery’s internal resistance is equal to 𝐼 times lowercase 𝑟, that internal resistance value. We can see, though, that this isn’t the whole story when it comes to emf. emf also includes the voltage supplied for the rest of the circuit. When we only consider one of these two terms in our description of emf, that description is incomplete. We won’t choose option (B) either.

Option (C) tells us that the emf of a battery is the current within the battery. But we’ve already seen that emf is a voltage, so calling it a current can’t be a correct description either. For this reason, we won’t choose option (C). This confirms our choice of option (D), that the emf of a battery is the potential difference across its terminals when it is not producing any current. And this agrees with our equation for emf because if we set the current 𝐼 to be zero, then emf equals 𝑉.

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