Series Networks

Example #1

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

1/C_ABC = 1/C_A + 1/C_B + 1/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:

1/C_ABC = 1/(12Ω) + 1/(4Ω) + 1/(6Ω) = 1/(2Ω).

Hence, C_ABC = 2Ω.

Example #2

Capacitors A, B and C are connected together in series. 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 capacitances of the individual capacitors:

1/C_ABC = 1/C_A + 1/C_B + 1/C_C.

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

1/(2Ω) = 1/C_A + 1/(5Ω) + 1/(10Ω).

Hence,

1/C_A = 1/(2Ω) - 1/(5Ω) - 1/(10Ω) = 1/(5Ω).

and so C_A = 5Ω.