Electromotive force and internal resistance (AQA A-Level Physics): Revision Notes

5.1.6 Electromotive force and internal resistance

Internal Resistance

• Definition: Batteries have an internal resistance $r$ , which is due to collisions between electrons and atoms inside the battery. As a result, some energy is lost as heat within the battery itself before the electrons leave, which can be represented as a small internal resistor.

Electromotive Force (EMF)

• Definition: EMF ($\varepsilon$) is the energy transferred per coulomb of charge by a cell. It represents the maximum energy that the battery can provide per unit charge, ideally without losses.
• Formula:

$$\varepsilon = \frac{E}{Q}$$

where $E$ is the energy transferred and $Q$ is the charge.

Total Circuit Resistance

• In a circuit, the total resistance $R_t$ is the sum of the internal resistance $r$ and the load resistance $R$ (resistance of external components). Therefore:

$$R_t = R + r$$

EMF and Potential Difference Relationships

• The EMF in the circuit can be expressed as:

$$\varepsilon = IR + Ir$$

where $IR$ is the potential difference across the load resistance (external components) and $Ir$ is the potential difference across the internal resistance.

• $IR$ (across $R$ ) is also called the terminal p.d. $( V )$.
• $Ir$ (across $r$ ) is known as lost volts ( $v$ ), which represents the energy lost inside the cell. Thus, the relationship between EMF and potential differences is:

$$\varepsilon = V + v$$

Measuring EMF

• To measure the EMF of a cell, use a voltmeter across the cell in an open circuit (i.e., no current is flowing). In this state, there are no lost volts, so the voltmeter reading is equal to the EMF.