Final answer:
Norton's theorem states that any two-terminal network of fixed resistances can be replaced with a current source and a parallel resistor. For two voltage sources with the same emfs but different internal resistances, if they supply the same current, the external resistance in the circuit with lower internal resistance must be higher. This is explained using the principles of series and parallel circuits and their equivalent resistances.
Step-by-step explanation:
The network theorem that states any two-terminal network of fixed resistances can be replaced by a current source and a parallel resistor is Norton's theorem. Norton's theorem is very similar to Thevenin's theorem, but while Thevenin's theorem uses a voltage source in series with a resistance, Norton's theorem utilizes a current source in parallel with a resistance.
To address the situation of two voltage sources, Source A and Source B, which have the same electromotive force (emf) but different internal resistances, we can infer that Source A has lower internal resistance than Source B. Therefore, if both sources supply the same current in their circuits, Source A must have a higher external resistance compared to Source B's circuit to still maintain the same current flow, given Ohm's Law (V = IR). Hence, the correct statement is that external resistance in Source A's circuit is more than in Source B's circuit.
It's important to note that these principles of network reduction involve the use of series and parallel circuits and their equivalent resistances to simplify complex circuits. This process allows for easier calculation and analysis of circuits by using equivalent models.