Question Video: Defining the Terminal Voltage of a Battery Physics

Which of the following statements is a correct description of the terminal voltage of a battery? [A] The terminal voltage of a battery is the voltage that it applies across a circuit to which it is connected. [B] The terminal voltage of a battery is the voltage of the battery when it’s fully discharged. [C] The terminal voltage of a battery is the voltage required to overcome its internal resistance. [D] The terminal voltage of a battery is the potential difference across its terminals when it’s not producing any current.

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Video Transcript

Which of the following statements is a correct description of the terminal voltage of a battery? (A) The terminal voltage of a battery is the voltage that it applies across a circuit to which it is connected. (B) The terminal voltage of a battery is the voltage of the battery when it’s fully discharged. (C) The terminal voltage of a battery is the voltage required to overcome its internal resistance. Or (D) the terminal voltage of a battery is the potential difference across its terminals when it’s not producing any current.

So we want to find which of these four statements describes the terminal voltage of a battery. Let’s start by recalling that a battery is a device which converts chemical energy into electrical energy. And we use batteries to provide a potential difference, or voltage, to a circuit. Now, when we’re talking about circuits in physics, we actually tend to use ideal cells instead of batteries. An ideal cell, which is represented by this symbol, doesn’t actually exist. It’s a theoretical component which we say can provide a constant voltage but which doesn’t have any resistance.

Batteries are used in real circuits to basically provide the same function as an ideal cell. However, they don’t behave in exactly the same way. This is because a battery has some electrical resistance, and we call this the internal resistance. And this means that a battery actually behaves more like an ideal cell and a resistor connected in series. The internal resistance of a battery, which we can label lowercase 𝑟, has some effects that we need to take into account whenever we’re talking about batteries. Specifically, the internal resistance of a battery actually decreases the potential difference that it’s able to provide to a circuit. Let’s clear some space at the top of the screen and see how this works.

Let’s start by thinking about the battery on its own, so it’s not connected to a circuit and there’s no charge flowing through it. Now, under these conditions, if we measure the potential difference between the positive and negative terminals of the battery, for example, by using a voltmeter, we would be measuring the emf, or electromotive force, of the battery. So the emf of the battery, which we can also represent with the symbol 𝜀, is the potential difference across the terminals of the battery when it’s not producing any current.

Things change when we connect our battery to a circuit. As soon as we do this, charge starts to flow. Specifically, negative charge in the form of electrons flows from the negative terminal of the battery moving around the circuit we’ve drawn in a clockwise direction before returning to the positive terminal of the battery.

Now we find that as soon as charge starts to flow, this actually changes the potential difference that’s measured between the terminals of the battery. The reason for this becomes clear once we remember that a battery has an internal resistance and that it behaves like an ideal cell and a resistor connected in series. The resistor that we’ve drawn here represents the internal resistance of the battery. Let’s label this internal resistance lowercase 𝑟. This ideal cell that we’ve drawn inside the battery represents the emf produced by the battery. So we can label it as having a potential difference equal to 𝜀. Now we know that when we connect this battery to a circuit, this produces a current in the circuit which we can label 𝐼.

It’s important to note that this current 𝐼 also exists within the battery itself. So within the battery, we effectively have charge flowing through a resistor. Whenever charge flows through resistor, we can think of the resistor as using up some of the voltage. Or in other words, any resistor in a circuit will have a potential difference drop across it. This means that as soon as we connect a battery to a circuit, the internal resistance of the battery will cause a potential difference drop. In other words, the potential difference supplied by a battery when it’s connected to a circuit will actually be less than the emf of the battery, that is, the potential difference across its terminals when it’s not connected to a circuit.

Now, the phrase terminal voltage is used to refer to the potential difference across a battery’s terminals while it’s in use. In other words, it’s the voltage that the battery applies across a circuit to which is connected. This terminal voltage is usually represented with the symbol 𝑉. The terminal voltage of a battery is always less than the battery’s emf because the battery’s internal resistance decreases the potential difference that can be supplied by the battery. The difference between the emf and the terminal voltage of the battery is equal to the potential difference drop due to the internal resistance of the battery. The size of this voltage drop is equal to the current in the circuit 𝐼 multiplied by the internal resistance lowercase 𝑟 of the battery.

And this quantity, which is measured in volts, is known as the lost volts. In other words, it’s the amount of potential difference which is lost due to the internal resistance of the battery. Looking at our answer options, we can see that option (A) matches the description we’ve just given of the terminal voltage. It’s the voltage, or potential difference, that a battery applies across a circuit to which it is connected. So, option (A) looks like it’s correct. But let’s take a look at the other options, too.

Option (B) says that the terminal voltage of a battery is the voltage of the battery when it’s fully discharged. Now, when a battery is fully discharged, its voltage is zero volts. That means that a battery that’s fully discharged isn’t capable of producing any current when it’s connected to a circuit. But we know that the terminal voltage of a battery refers to the potential difference across a battery when it’s actually producing a current within a circuit. So, we know that option (B) isn’t the correct answer.

Option (C) says that the terminal voltage of a battery is the voltage required to overcome its internal resistance, but we know that this isn’t the correct definition either. In fact, this is the definition of the lost volts of the battery in a circuit. Finally, option (D) says that the terminal voltage of a battery is the potential difference across its terminals when it’s not producing any current. However, we now know that this definition actually corresponds to the emf, or electromotive force, of the battery. So, given that (C) and (D) are not the correct answer options either, we know that option (A) is correct after all. The terminal voltage of a battery is the voltage that it applies across a circuit to which is connected.

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