As we know that no current flows in a conductor unless a device (such as a battery) imparts energy to the free electrons. We say that the battery is the source of an electron-moving force or electromotive force, usually abbreviated to EMF.
Electromotive force is a property that distinguishes an energy source from the rest of a circuit.
To help understand the relationship between energy and flow, consider the operation of the hydroelectric generating station shown in Figure 1.
Water enters a tunnel at the base of the dam, flows down through a turbine, and then discharges into the river below. In falling 100 m, the water loses some of its gravitational potential energy while gaining kinetic energy.
The turbine transfers some of this kinetic energy to the generator or dynamo, which converts most of it into electric energy.
Figure 1 Simplified cross-section of a hydroelectric generating station
Since objects at the surface of the earth are 6400 km away from the earth’s center of gravity, the difference in gravitational force acting on a cubic meter of water above and below the generating station is negligible. But there is an appreciable difference in the potential energy of a cubic meter of water above and below the station.
The law of conservation of energy requires the difference in potential energy between a unit quantity of water above and below the generating station to be equal to the energy expended in raising the unit quantity of water the 100 m against the force of gravity.
Figure 2 shows the electric circuit with the battery turned on its side to parallel the water flow in Figure 1.
Figure 2 Electric potential difference
The free electrons in the conductor flow away from the negative terminal of the battery and toward the positive terminal.
To maintain the negative and positive charges at the two battery terminals, an equivalent number of electrons must move inside the battery from the positive terminal to the negative terminal. These electrons move away from the positive terminal and toward the negative terminal. So, the electrons inside the battery move against the electric forces acting on them, just as water moves against gravitational force when it is pumped uphill.
The electrons acquire potential energy at the expense of the chemical energy stored in the battery. Consequently, an electron moving inside the battery has a greater potential energy when it arrives at the negative terminal than when it leaves the positive terminal.
There is an electric potential difference between the negative and positive terminals of the battery, with electrons at the negative terminal being at a higher potential than those at the positive terminal.
Under the influence of gravity, the water in the hydroelectric generating station of Figure 1 always tends to fall to a lower potential energy level.
Similarly, electrons at the negative terminal of an energy source tend to “fall” to a lower potential energy level. They can move to a lower potential via the external conductor connected between the battery terminals.
When flowing from the negative terminal to the positive terminal through the external circuit, electrons lose as much potential energy as they gained in being moved inside the battery from the positive terminal to the negative terminal. This energy “lost” in the external circuit is converted into light, heat, or some other form of energy, depending on the nature of the circuit.
Electric Potential Difference Definition
In traveling the complete circuit around the closed loop of Figure 2, electrons experience a potential rise within the battery and a matching potential fall or the potential drop in the circuit.
The electric potential difference between any two points in a circuit is the rise or fall in potential energy involved in moving a unit quantity of charge from one point to the other. The letter symbol for the potential difference is E or V.
EMF is the energy per unit of charge that a battery or other energy source converts in the process of creating a potential difference between its terminals.
Since a force has dimensions of mass times acceleration, EMF is not actually a force. Electromotive force is a traditional term that is gradually disappearing from common use.
The Volt
Work is energy transferred to a body or system. For example, the force of gravity does work on a falling body. This work increases the kinetic energy of the body and decreases its potential energy.
The letter symbol for work and energy is W.
The joule (symbol J) is the SI unit of work and energy.
One joule is equal to one newton meter: 1 J = 1 N.m = 1 kg.m2/s2.
When a force moves a body, the work, W, done is equal to the magnitude, F, of the force times the distance, d, the body moves:\[W\text{ }=\text{ }Fd\]
We can express the electric potential difference in terms of joules per coulomb, or volts.
The volt (symbol V) is the SI unit of potential difference.
The potential difference between two points is one volt if one coulomb of charge gains or loses one joule of energy when moving from one point to the other: 1 V = 1 J/C.
This equation relates potential difference to charge and energy:
\[\begin{matrix} E=\frac{W}{Q}~~~~~~~ & or & V=\frac{W}{Q} \\\end{matrix}\]
Where E (or V) is potential difference in volts, W is energy in joules, and Q is charge in coulombs.
Note that EMF is measured in volts, while a force is measured in newtons.
Voltage Example 1
A power supply delivers 55 J when 50 C of electrons move from its negative terminal to its positive terminal. Find the potential difference between the terminals.
Solution
\[E=\frac{W}{Q}=\frac{55J}{50C}=1.1V\]
Voltage Example 2
A current of 0.30 A flowing through the filament of a cathode-ray tube produces 9.45 J of heat in 5.0 s. What is the potential difference across the filament?
Solution
Since,
\[I=\frac{Q}{t}\]
\[Q=It=0.30A\times 5s=1.5C\]
\[V=\frac{W}{Q}=\frac{9.45J}{1.5C}=6.3V\]
EMF, Potential Difference, and Voltage
EMF is the energy converted per unit quantity of electric charge moved from one terminal to the other inside the source.
However, the EMF is equal to the potential rise between the terminals of the source when the circuit is open and no current flows (I = 0).
When current flows in the circuit, inefficiencies in the energy-conversion process make the potential rise less than the internal EMF of the source.
In the circuit shown in Figure 3, the left voltmeter measures the potential difference between the battery terminals. Even with the switch open, this potential difference is not the same as the EMF of the battery since the voltmeter itself draws some current from the battery.
Figure 3 Measuring source voltage and voltage drop in a basic electric circuit
For many circuit calculations, the energy source is assumed to be perfectly efficient, making its internal EMF and the potential difference between its terminals equal. Nonetheless, we should not use the term EMF to refer to the potential rise between the terminals of a generating device.
The term voltage is now commonly used as a simpler expression for potential difference. We can maintain the distinction between rising and fall in potential by using the terms source voltage or applied voltage for the potential rise between the terminals of a source and the term voltage drop for the potential fall across the circuit load.
Voltage Symbol
The letter symbol for source voltage or applied voltage is E. The letter symbol for voltage drop is V.
The difference between a source voltage and a voltage drop is illustrated in Figure 3.
When the switch is closed, both voltmeters show the same reading since the current through the lamp creates a voltage drop across the lamp equal to the source voltage (or applied voltage).
When the switch is open, the voltmeter connected to the battery terminals still registers the source voltage, but the voltmeter connected to the lamp terminals reads zero. A voltage drop can appear across the lamp only when electrons are flowing through it.
Important Point
A voltage or potential difference must be measured between two points, from one point with respect to another, or across a circuit element. There is no such thing as a “voltage at a point.” On the other hand, we speak of electric current in or through a conductor or other component.
