Which of the following statements is a correct description of the lost voltage of a battery? (A) The lost voltage of a battery is the potential difference across its terminals when it is not producing any current. (B) The lost voltage of a battery is the voltage of the battery when it is fully discharged. (C) The lost voltage of a battery is the voltage required to overcome its internal resistance. (D) The lost voltage of a battery is the voltage that it applies across a circuit that it is connected to.
Clearing some space at the top of our screen, let’s consider a battery that’s part of a simple electrical circuit. Through chemical means, this battery supplies a potential difference to the circuit. That is, it causes the electrical potential here in the circuit at the battery’s positive terminal to be different than the electrical potential here at the battery’s negative terminal. In order to create this potential difference, the battery must work against some internal resistance. That is, not only is there’s resistance externally in the circuit the battery is connected to, but there’s also some resistance in the battery itself to generating a potential difference.
If we were to use a measuring device, say a voltmeter or a multimeter, to measure the potential difference across the terminals of a battery, we would be measuring what is called the terminal voltage of the battery. We can call this 𝑉 sub t. The battery’s terminal voltage is the potential difference experienced by the rest of the circuit. The terminal voltage, however, reflects a decrease in potential difference across the battery due to what is called lost voltage.
As we mentioned, a battery is a circuit component that has its own internal resistance. We could think of a battery then as a cell connected to a resistor. The cell generates a potential difference, and the resistor decreases that difference. The true potential difference generated by a battery is called its emf, its electromotive force. emf is diminished by a battery’s internal resistance, and the amount it’s diminished is called lost voltage.
It’s possible to connect emf and terminal voltage using an equation. If the internal resistance of our battery is lowercase 𝑟, then the terminal voltage, the voltage across the battery’s terminals when it’s in operation, is equal to the emf the battery generates minus the current in the circuit multiplied by the battery’s internal resistance. This product, 𝐼 times 𝑟, is the lost voltage of our battery. As stated in answer choice (C), this is the voltage required to overcome the battery’s internal resistance.
It looks then that choice (C) will be our answer. Answer choice (D), which says that the lost voltage of a battery is the voltage the battery applies across a circuit that it’s connected to, is not correct because we know that that voltage is actually the terminal voltage, 𝑉 sub t, of the battery. Considering answer choice (B), the voltage of the battery when it’s fully discharged is zero volts. This, however, is not what we mean when we talk about the lost voltage of a battery. Considering answer option (A), even if we disconnect a battery from any circuit and then measure the potential difference across its terminals, that will still just give us the terminal voltage, 𝑉 sub t, of the battery. Answer choice (A) is not correct either.
Option (C) is confirmed as our answer. The lost voltage of a battery is the voltage required to overcome its internal resistance.