Electromotive Force & Internal Resistance (HL IB Physics)

• 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 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:

• Emf is also the potential difference across the cell when no current is flowing
• The emf of a cell can be measured by connecting a high-resistance voltmeter around the terminals of the cell in an open circuit

Emf is measured using a voltmeter connected in parallel with the cell

• 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 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
  • 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 its 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:

• Where:
  • ε = electromotive force (emf) (V)
  • I = current (A)
  • R = resistance available to the rest of the circuit (Ω)
  • r = internal resistance (Ω)

• Emf is, therefore, the total, or maximum, voltage available to the circuit