The internal resistance of a source is the loss of potential difference per unit current in the source when current passes through the source.
Due to the opposition to the flow of charge through the source energy is dissipated as heat inside the source.
In circuit diagrams the internal resistance is shown as a small resistor in series with the source.
where ε is the e.m.f. and V is the p.d. across the components.
There is a loss of p.d. per unit current when current passes through the source. The lost volts = ε - V
ε = Ir + IR
where R is the total resistance of the circuit and r is the internal resistance of the source and I is the current.
The e.m.f. of the source = lost volts + p.d. across the components.