• When charge passes through a power supply such as a battery, it?gains?electrical energy
• The?electromotive force (e.m.f)?is defined as:

The amount of chemical energy converted to electrical energy per coulomb of charge (C) when passing through a power supply

• This can also be written as:

• 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)

   

• 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

• 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 work done per unit charge / coulomb to overcome the internal resistance / resistance inside the battery (when current flows)

• • In other words, this is 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

• All power supplies have some resistance between their terminals
  • This is called?internal resistance?(r)

   

• Internal resistance is defined as:

The resistance of the materials within the battery

• 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

• Where:
  • Resistor?R?is the 'load resistor'
  • r?is the internal resistance
  • ε?is the e.m.f
  • Vr?is the lost volts
  • VR?is the p.d across the load resistor, which is the same as the terminal p.d