# 4.4.1 E.m.f & Internal Resistance

### E.m.f & Internal Resistance

• 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

• E.m.f can be represented by the symbol ε (greek letter epsilon)
• It is not actually a force, and is measured in volts (V)
• The e.m.f source is from a battery or a power supply
• 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

#### 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

• Resistor R is referred to as the ‘load resistor’

### Terminal p.d & Lost Volts

• The terminal potential difference (p.d) is the potential difference across the terminals of a cell
• If there was no internal resistance, the terminal p.d would be equal to the e.m.f
• It is defined as:

V = IR

• Where:
• V = terminal p.d (V)
• I = current (A)
• R = resistance (Ω)
• Since a cell has internal resistance, the terminal p.d is always lower than the e.m.f

• In a closed circuit, current flows through a cell and a potential difference develops across the internal resistance
• Since resistance opposes current, this reduces the energy per unit charge (voltage) available to the rest of the external circuit
• This difference 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)
• Therefore, lost volts is the difference between the e.m.f and the terminal p.d

#### 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, then the e.m.f equations must be used.

Close