# 5.4.1 Electromotive Force & Internal Resistance

### Electromotive Force

• When charge passes through a power supply such as a battery, it gains electrical energy
• The electromotive force (e.m.f) is the amount of chemical energy converted to electrical energy per coulomb of charge (C) when charge passes through a power supply

• This can also be written as:

• E.m.f can be represented by the symbol ε (greek letter epsilon), or capital E
• Note that e.m.f is not actually a force. It is measured in volts (V)
• E.m.f is equal to the potential difference across the cell when no current is flowing
• E.m.f can be measured by connecting a high-resistance voltmeter around the terminals of the cell in an open circuit, as so:

e.m.f is measured using a voltmeter connected in parallel with the cell

• V is the terminal potential difference
• This is the voltage available in the circuit itself

V = IR

• Where:
• V = terminal p.d (V)
• I = current (A)
• R = resistance (Ω)

• When a load resistor is connected, current flows through the cell and a potential difference develops across the internal resistance
• This voltage is not available to the rest of the circuit so is called the ‘lost volts’
• Lost volts is usually represented by little v
• It is defined as the voltage lost in the cell due to internal resistance, so, from conservation of energy:
• v = e.m.f − terminal p.d

v = ε – V = Ir (Ohm’s law)

• Where:
• v = lost volts (V)
• I = current (A)
• r = internal resistance of the battery (Ω)
• ε = e.m.f (V)
• V = terminal p.d (V)
• The e.m.f is the sum of these potential differences, giving the equation below:

• E.m.f can therefore be defined as the total, or maximum, voltage available to the circuit

### Internal Resistance

• All power supplies have some resistance between their terminals
• This is called internal resistance (r)
• It is internal resistance that causes the charge circulating to dissipate some electrical energy from the power supply itself
• This is why the cell becomes warm after a period of time
• Therefore, over time the internal resistance causes loss of voltage or energy loss in a power supply
• A cell can be thought of as a source of e.m.f with an internal resistance connected in series. This is shown in the circuit diagram below:

Circuit showing the e.m.f and internal resistance of a power supply

#### Worked Example

A battery of e.m.f 7.3 V and internal resistance r of 0.3 Ω is connected in series with a resistor of resistance 9.5 Ω.

Determine:
a)     The current in the circuit
b)     Lost volts from the battery

#### Exam Tip

If the exam question states ‘a battery of negligible internal resistance’, this assumes that e.m.f of the battery is equal to its voltage. Internal resistance calculations will not be needed here.

If the battery in the circuit diagram includes internal resistance (like that in the worked example), then the e.m.f equations must be used.

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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