Electromotive Force & Internal Resistance (AQA AS Physics): Revision Note

Electromotive force

• When charge passes through a power supply such as a battery, it gains electrical energy

• 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

$\mathrm{E}.\mathrm{m}.\mathrm{f}=\frac{\mathrm{Energy}\mathrm{transformed}\mathrm{from}\mathrm{other}\mathrm{forms}\mathrm{to}\mathrm{electrical}}{\mathrm{Charge}}$

• This can also be written as:

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

• 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:

• 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

$v=\epsilon -V=Ir$ (Ohm’s law)

• Where:

  • $v$ = lost volts (V)

  • $I$ = current (A)

  • $r$ = internal resistance of the battery (Ω)

  • $\epsilon$ = e.m.f (V)

  • $V$ = terminal p.d (V)

• The e.m.f is the sum of these potential differences, giving the equation below:

$\epsilon =IR\hspace{0.17em}+\hspace{0.17em}Ir=I\left(R\hspace{0.17em}+\hspace{0.17em}r\right)$

• Where:

  • $IR$ is the terminal p.d (V)

  • $Ir$ is the lost volts (V)

  • $R$ = resistance of load (Ω)

• 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)

• 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:

• Where:

  • Resistor $R$ is the 'load resistor'

  • $r$ is the internal resistance

  • $\epsilon$ is the e.m.f

  • $V_r$ is the lost volts

  • $V_R$ is the p.d across the load resistor, which is the same as the terminal p.d