Parallel Networks

Example #1

Capacitors A, B and C are connected together in parallel. Together, they are equivalent to the single capacitor on the left labeled ‘ABC’. The capacitance of the entire three-capacitor network is equal to the sum of the individual capacitances in the network:

C_ABC = C_A + C_B + C_C

where C_ABC, C_A, C_B and C_C are the capacitances of capacitors ABC, A, B and C respectively. Substituting in the values from the diagram gives:

C_ABC = 4F + 3F + 2F = 9F.

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 capacitance of the entire two-capacitor network is equal to the sum of the capacitances of the individual capacitors:

C_AB = C_A + C_B

where C_AB, C_A and C_B are the capacitances of capacitors AB, A and B respectively. Substituting in the values from the diagram gives:

5F = C_A + 4F.

Solving gives C_A = 1F.