Capacitors A, B and C are connected together in series. The voltage across the entire three-capacitor network is equal to the sum of the voltages across the individual capacitors. Hence the voltage across the three-capacitor network is:
3V + 4V + 5V = 12V.
The three-capacitor network containing capacitors A, B and C is equivalent to the capacitor on the left labeled ‘ABC’. The word ‘equivalent’ means that the voltage, charge and capacitance of capacitor ABC are equal to the voltage, charge and capacitance of the three-capacitor series network. Hence, the voltage across the equivalent capacitor is equal to 12V.
Capacitors A, B and C are connected together in series. Together, they are equivalent to the single capacitor on the left labeled ‘ABC’. The word ‘equivalent’ means that the voltage, charge and capacitance of capacitor ABC are equal to the voltage, charge and capacitance of the three-capacitor series network. In particular,
VABC = VA + VB + VC.
where VABC, VA, VB and VC are the voltages across capacitors ABC, A, B and C respectively. Substituting values gives:
16V = VA + 4V + 5V.
Solving for VA reveals that VA = 7V.