Difference Between EMF and Potential Difference

Main Difference – EMF vs. Potential Difference

The terms EMF and potential difference both describe energy transfers involving electrons in a circuit. The main difference between EMF and potential difference is that EMF refers to the amount of electrical energy gained by a coulomb of charge as it goes around a circuit, whereas Potential Difference describes the amount of electrical energy lost by a coulomb of charge.

What is EMF

EMF ( $\varepsilon$ ) stands for electromotive force. In a cell or a generator, the EMF refers to the amount of electrical energy given to each coulomb of electrons. This electrical energy has been created by conversion of another form of energy into electrical energy (e.g. chemical energy to electrical energy in a cell, or mechanical energy to electrical energy in a generator).

Note that even though the word force is included, EMF has nothing to do with force. Rather, the term is concerned with the gain and loss of electrical energy by electrons.

What is Potential Difference

In an electrical circuit, the potential difference $V$ between any two points in the circuit is the energy lost by a coulomb of charge as it travels between those two points. Potential difference can be measured using a voltmeter, and it is expressed in units of volts.

So, the term EMF is used to describe instances where electrons gain electrical energy, whereas the potential difference is used to describe instances where electrons lose their electrical energy. Around a closed loop in a circuit, energy has to be conserved, so this leads to Kirchoff’s second law, which states that the sum of EMFs around a closed loop is equal to the sum of potential differences around that loop.

If a cell is ideal, then it gives electrical energy to electrons passing through it and these electrons come out of the cell without losing any of the electrical energy that they have acquired. However, in reality, electrons lose some of the energy that they gain before they even leave the cell. We say that the energy has been lost due to the internal resistance in the cell. In circuit analysis, it is useful to imagine that this internal resistance comes from a resistor inside the cell:

Difference Between EMF and Potential Difference - Internal_resistance

An ideal cell (left) and a real cell (with internal resistance) (right)

The terminal potential difference across a cell refers to the energy gained by a coulomb of electrons as they pass through it, minus the energy they lose due to internal resistance. If the EMF is $\varepsilon$ , the internal resistance is $r$ , the current through the cell is $I$ then the terminal potential difference $V$ given by: