Electromotive force (EMF) is an unfamiliar concept to most people, but it’s closely linked to the more familiar concept of voltage. Understanding the difference between the two and what EMF means gives you the tools you need solve many problems in physics and electronics, and introduces the concept of the internal resistance of a battery. EMF tells you the voltage of the battery without the internal resistance reducing the value as it does for ordinary potential difference measurements. You can calculate it in a couple of different ways, depending on what information you have.
TL;DR (Too Long; Didn't Read)
Calculate EMF using the formula:
ε = V + Ir
Here (V) means the voltage of the cell, (I) means the current in the circuit and (r) means the internal resistance of the cell.
What Is EMF?
The electromotive force is the potential difference (i.e., voltage) across the terminals of the battery when no current is flowing. This might not seem like it would make a difference, but every battery has “internal resistance.” This is like the ordinary resistance that reduces the current in a circuit, but it exists within the battery itself. This is because the materials used to make up the cells in the battery have their own resistance (since essentially all materials do).
When no current is flowing through the cell, this internal resistance doesn’t change anything because there is no current for it to slow down. In a way, the EMF can be thought of as the maximum potential difference across the terminals in an idealized situation, and it’s always bigger than the voltage of the battery in practice.
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Equations for Calculating EMF
There are two main equations for calculating EMF. The most fundamental definition is the number of joules of energy (E) each coulomb of charge (Q) picks up as it passes through the cell:
ε = E ÷ Q
Where (ε) is the symbol for electromotive force, (E) is the energy in the circuit and (Q) is the charge of the circuit. If you know the resulting energy and the amount of charge passing through the cell, this is the simplest way to calculate EMF, but in most cases you won’t have that information.
Instead, you can use the definition more like Ohm’s law (V = IR). This can be expressed as:
ε = I (R + r)
With (I) meaning current, (R) for the resistance of the circuit in question and (r) for the internal resistance of the cell. Expanding this reveals the close link with Ohm’s law:
ε = IR + Ir
= V + Ir
This shows you can calculate the EMF if you know the voltage across the terminals (the voltage as used in real-world situations), the current flowing and the internal resistance of the cell.
How to Calculate EMF: An Example
As an example, imagine you have a circuit with a potential difference of 3.2 V, with a current of 0.6 A flowing and the internal resistance of the battery at 0.5 ohms. Using the formula above:
ε = V + Ir
= 3.2 V + 0.6 A × 0.5 Ω
= 3.2 V + 0.3 V = 3.5 V
So the EMF of this circuit is 3.5 V.