10.1.3 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 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

• V_R is the terminal potential difference
  • This is the voltage available in the circuit itself
  • Terminal p.d = I × R (Ohm’s law)

• When a load resistor is connected, current flows through the cell and a potential difference develops across the internal resistance. This voltage is not available to the rest of the circuit so is called the ‘lost volts’
• V_r is the lost volts
  • This is the voltage lost in the cell due to internal resistance, so, from conservation of energy:
  • Lost volts = e.m.f − terminal p.d
  • Lost volts = I × r (Ohm’s law)

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

e.m.f equation

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