Capacitors A, B and C are connected together in parallel. The charge of the entire three-capacitor network is equal to the sum of the charges of the individual capacitors. Hence the total charge of the three-capacitor network is:
QA + QB + QC = 4C + 5C + 6C = 15C.
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 charge of equivalent capacitor ABC is equal to 15C.
Capacitors A and B are connected together in parallel. Together, they are equivalent to the single capacitor on the left labeled ‘AB’. The word ‘equivalent’ means that the voltage, charge and capacitance of capacitor AB are equal to the voltage, charge and capacitance of the two-capacitor parallel network. In particular,
QAB = QA + QB
where QAB, QA and QB are the charges of capacitors AB, A and B respectively. Substituting values gives:
8C = QA + 3C.
Solving for QA reveals that QA = 5C.