Video Transcript
A battery is connected to a circuit with a resistance of 4.25 ohms. The current in the circuit is 0.755 amperes. The internal resistance of the battery is 0.635 ohms. What is the electromotive force of the battery? Give your answer to two decimal places.
Let’s say that this is our battery, and here is the circuit it’s connected to. We’re told this circuit has a resistance, we’ll call it 𝑅, of 4.25 ohms. The current in the circuit, we’ll call it 𝐼, is 0.755 amperes. And the battery itself, we’re told, has some resistance called its internal resistance, which we’ll refer to with a lowercase 𝑟. We want to solve for the electromotive force, or emf, of the battery. Despite its name, electromotive force actually describes an electrical potential difference. As such, we can usefully apply Ohm’s law to our situation. This law says that the potential difference 𝑉 across an electrical circuit is equal to the current in that circuit 𝐼 multiplied by the total circuit resistance 𝑅.
For our purposes, we can replace 𝑉 with emf. We’ve called the current in our circuit capital 𝐼. And we see that our total circuit resistance is the sum of capital 𝑅 and lowercase 𝑟. In other words, it’s the sum of the total resistance of the external circuit and the internal resistance of our battery. Substituting in values, we know that 𝐼 is 0.755 amperes, capital 𝑅 is 4.25 ohms, and lowercase 𝑟, the internal resistance, is 0.635 ohms. Adding together these two resistances, we get 4.885 ohms as our total circuit resistance.
Multiplying these values together and rounding to two decimal places, we find a result of 3.69 volts. This is the emf, or the electromotive force, of our battery.
