Electromotive Force (EMF)
When you connect a battery to a circuit, charges begin to flow. But what actually drives them? The answer is electromotive force, or EMF. Despite the name, EMF is not a force at all — it is a measure of energy. Specifically, EMF is the energy supplied per unit charge by a source such as a battery, solar cell, or generator. It tells you how many joules of electrical energy a source provides for every coulomb of charge that passes through it. The unit of EMF is the volt (V), the same as potential difference. Think of a battery like a water pump in a pipe system. Water (charge) doesn't flow on its own uphill — the pump (battery) does work on the water to push it around the circuit. EMF is a measure of how hard that pump works per unit volume of water it moves. A 12 V car battery gives 12 joules of energy to every coulomb of charge that passes through it. This energy is then converted into other forms — heat, light, sound — by the components in the circuit. EMF is therefore a property of the source, not the external circuit. It is important to distinguish EMF from terminal voltage. EMF (ε) is the total energy per coulomb delivered by the source. Terminal voltage is the potential difference available at the battery's terminals when current flows, which is always less than the EMF because some energy is lost inside the battery itself due to its internal resistance. Understanding this distinction is essential for analysing real circuits.
- Energy and Charge
- The Source of EMF
- Internal Resistance
- EMF in a Complete Circuit
- Measuring EMF
Energy and Charge
EMF is defined as the work done (energy transferred) by the source per unit positive charge driven around the complete circuit. If a source does W joules of work moving Q coulombs, then ε = W/Q. For example, if a battery does 24 J of work moving 2 C of charge, its EMF is 12 V.
The Source of EMF
A battery's EMF arises from chemical reactions inside it. These reactions separate positive and negative charges, creating a potential difference between the terminals. In a solar cell, it is photons knocking electrons free. In a generator, it is a conductor moving through a magnetic field. In every case, some non-electrical energy is converted into electrical potential energy for the charges.
Internal Resistance
No real battery is perfect. The materials inside have electrical resistance — called internal resistance, r. When current I flows, this internal resistance causes a voltage drop of Ir inside the battery itself. This means the terminal voltage V = ε − Ir is always less than the EMF when current flows. Only when the circuit is open (I = 0) does the terminal voltage equal the EMF.
EMF in a Complete Circuit
Using Kirchhoff's voltage law around the complete loop: the EMF equals the sum of all voltage drops. If the external resistance is R, then ε = IR + Ir = I(R + r). This single equation encapsulates the relationship between EMF, current, external resistance, and internal resistance. Rearranging gives the current in the circuit: I = ε / (R + r), which is one of the most useful equations in circuit analysis.
Measuring EMF
You can measure the EMF of a battery by connecting a high-resistance voltmeter directly across its terminals with no other load connected. Because the voltmeter draws negligible current (I ≈ 0), the voltage drop across internal resistance is negligible, so the voltmeter reads approximately ε. To find internal resistance, measure terminal voltage at different currents and plot V against I — the y-intercept gives ε and the magnitude of the slope gives r.
The Key Equation
- \varepsilon — Electromotive Force (EMF) (Volt (V)): The total energy supplied per unit charge by the source; measured in volts.
- W — Work done (Joule (J)): The total electrical energy transferred by the source to the charges.
- Q — Charge (Coulomb (C)): The total charge that passes through the source.
- I — Current (Ampere (A)): The rate of flow of charge around the circuit.
- R — External resistance (Ohm (Ω)): The total resistance of the components outside the battery.
- r — Internal resistance (Ohm (Ω)): The resistance of the battery's own internal materials, which causes energy loss inside the source.
Worked Example
Problem. A battery has an EMF of 9.0 V and an internal resistance of 0.5 Ω. It is connected to an external resistor of 8.5 Ω. Calculate: (a) the current in the circuit, and (b) the terminal voltage of the battery.
Answer. Current I = 1.0 A; Terminal voltage V = 8.5 V
Origins · 1 minAlessandro Volta and how this was discovered
Alessandro Volta invented the voltaic pile in 1800 — the world's first true battery — demonstrating that a sustained electric current could be produced by chemical means. His device, alternating discs of zinc and copper separated by brine-soaked cloth, was the first source of steady EMF. The concept of electromotive force is directly tied to his discovery, and the unit of voltage, the volt (V), is named in his honour. Napoleon Bonaparte was so impressed by Volta's battery that he made Volta a Count and invited him to demonstrate his invention before the French National Institute. Volta performed the demonstration in Paris in 1801.
Related Concepts
- Terminal Voltage — Terminal voltage is the measurable potential difference at a battery's terminals when current flows, directly related to EMF by the equation V = ε − Ir.
- Internal Resistance — Internal resistance is the resistance within the source itself; it determines how much of the EMF is 'lost' inside the battery rather than delivered to the external circuit.
- Ohm's Law — Ohm's Law (V = IR) is used together with EMF equations to calculate current and voltage in circuits containing cells.
- Kirchhoff's Voltage Law — Kirchhoff's Voltage Law states that the sum of EMFs around a loop equals the sum of potential drops, making it the formal basis for the EMF circuit equation.