# Potential and Potential Difference

As a charge moves round a circuit from the positive to the negative it loses energy. There is a problem here. As you know an electric current is a flow of negatively charged electrons and these flow away from the negative terminal of a supply, round the circuit and back to the positive terminal. However the 'traditional' view of current flow is from positive to negative and we will take that view when looking at the energy of electrical charge.

We define the amount of electrical potential energy that a unit charge has as:

The electrical potential energy of a unit charge at a point in a circuit is called the potential at that point.

The next set of diagrams (Figure 2) show how the potential varies round some basic circuits. To simplify the treatment we are going to assume that the energy lost in the connecting wires is negligible and we are going to ignore it. This means that the energy of the charge at one end of a connecting wire is the same as that at the other end. The bigger the energy change the bigger the difference in potential. We call the difference in electrical potential between two points in the circuit the potential difference between those two places.

The potential difference between two points is defined as:

Potential difference between two points in a circuit is the work done in moving unit charge (i.e. one coulomb) from one point to the other

The units for potential difference are Joules per coulomb, or volts. (1 volt = 1 Joule/coulomb).

Figure 2(a) shows the variation in the potential around the circuit. We can follow this by considering each section of the circuit in turn.

Along the connecting wire from the cell to B there is no resistance and so no loss of electrical energy or drop in potential.

In the resistors r and R energy is converted to heat and so the potential drops from B through to E.

From E to the cell there is no loss of electrical energy and so the potential at E is the same as that at the negative terminal of the cell – zero.

Figures 2(b and c) shows that when no current flows in a circuit there is no change of potential and therefore no potential difference between two parts of that circuit that are connected.

So if a charge Q moves between two points in a circuit that have a potential difference of V volts between them the energy gained (or lost) by the charge is given by the formula:

Electrical energy = Charge x Potential difference(Voltage) Joules = Coulombs x Volts = Amps x Time x Volts

But since Q = It we have:

Electrical energy = ItV

Example problems
Calculate the amount of energy supplied by a 4.5 V battery when:
(a) a charge of 20 C passes through it
(b) a current of 25 mA flows through is for 3 minutes (a) Energy = potential difference x charge = 4.5 x 20 = 90 J
(b) Energy = potential difference x charge = potential difference x current x time
Therefore:
Energy = 4.5 x 25x10-3 x 180 = 20.25 J