Because resistors A, B and C are connected together in series, they all have the same current, both in terms of values and directions. Since the current through resistor A is directed to the left, the currents through both of the resistors B and C are also directed to the left.
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. In particular, the current which is directed to the left through the three resistor network must also be directed to the left through resistor ABC. Thus the current thru resistor ABC is directed to the left.
Resistors A and B are connected together in series. 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 series network. In particular, the current that is directed to the left through resistor AB must also be directed to the left through both resistors A and B. Thus the currents through resistors A and B are both directed to the left.