Resistors A, B and C are connected together in parallel. The current through the entire three-resistor network is equal to the sum of the currents through the individual resistors. Hence the total current through the three-resistor network is:
4A + 5A + 6A = 15A.
The three-resistor network containing resistors A, B and C is equivalent to the resistor on the left labeled ‘ABC’. The word ‘equivalent’ means that the voltage, current and resistance of resistor ABC are equal to the voltage, current and resistance of the three-resistor series network. Hence, the current through equivalent resistor ABC is equal to 15A.
Resistors A, and B are connected together in parallel. Together, they are equivalent to the single resistor on the left labeled ‘AB’. The word ‘equivalent’ means that the voltage, current and resistance of resistor AB are equal to the voltage, current and resistance of the two-resistor parallel network. In particular,
IAB = IA + IB
where IAB, IA and IB are the currents through resistors AB, A and B respectively. Substituting values gives:
8A = IA + 3A.
Solving for IA reveals that IA = 5A.