Electromotive Force & Internal Resistance (DP IB Physics: HL): Revision Note

Electromotive Force

• When a 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 when a charge passes through a power supply

• Cells and batteries provide a source of e.m.f.

• E.m.f. is measured in volts (V) and can be calculated using:

• E.m.f. is also the potential difference across the cell when no current is flowing

• The e.m.f. of a cell can be measured by connecting a high-resistance voltmeter across the terminals of the cell in an open circuit

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)

• This internal resistance 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

• The internal resistance, therefore, causes a loss of voltage or energy in a power supply

• A cell can be considered 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

  • 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

• V_r is called the 'lost volts' as it's the potential difference 'lost' due to the internal resistance in the cell

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

$\epsilon =I\left(R+r\right)$

• Where:

  • ε = electromotive force (emf) (V)

  • I = current (A)

  • R = resistance available to the rest of the circuit (Ω)

  • r = internal resistance (Ω)

• E.m.f. is, therefore, the total, or maximum, voltage available to the circuit