Parallel Networks

Example #1

Because capacitors A, B and C are connected together in parallel, they all have the same voltage. Since the voltage across capacitor A is 4V, the voltages across both of the capacitors B and C are also 4V.

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 parallel network. In particular, the 4V across each of the capacitors in the three-capacitor network must be the same as the voltage across capacitor ABC. Thus, the voltage across capacitor ABC is also 4V.

Example #2

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, the 3V voltage across capacitor AB must equal the voltage across capacitor A as well as the voltage across capacitor B. Thus the voltages across capacitors A and B are both 3V.