Series Networks

Example #1

Resistors A, B and C are connected together in series. Together, they are equivalent to the single resistor on the left labeled ‘ABC’. The resistance of the entire three-resistor network is equal to the sum of the resistances across the individual resistors:

R_ABC = R_A + R_B + R_C.

where R_ABC, R_A, R_B and R_C are the resistances of resistors ABC, A, B and C respectively. Substituting in the values from the diagram gives:

R_ABC = 3Ω + 4Ω + 5Ω = 12Ω.

Example #2

Resistors A, B and C are connected together in series. Together, they are equivalent to the single resistor on the left labeled ‘ABC’. The resistance of the entire three-resistor network is equal to the sum of the resistances of the individual resistors:

R_ABC = R_A + R_B + R_C.

where R_ABC, R_A, R_C and R_C are the resistances of resistors ABC, A, B and C respectively. Substituting in the values from the diagram gives:

16Ω = R_A + 4Ω + 5Ω.

Solving for R_A reveals that R_A = 7Ω.