Resistors A, B and C are connected together in series. The voltage across the entire three-resistor network is equal to the sum of the voltages across the individual resistors. Hence the voltage across the three-resistor network is:
3V + 4V + 5V = 12V.
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 voltage across the equivalent resistor is equal to 12V.
Resistors A, B and C are connected together in series. Together, they are equivalent to the single 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,
VABC = VA + VB + VC.
where VABC, VA, VB and VC are the voltages across resistors ABC, A, B and C respectively. Substituting values gives:
16V = VA + 4V + 5V.
Solving for VA reveals that VA = 7V.