Equivalent resistance of a series association

What is a series association?

Two (or more) resistors are said to be in series when they are connected "end to end," on a single branch of the circuit, with no branching point between them. Direct consequence: they are traversed by the same electric current I.

The law of addition of resistances

For n resistors R1, R2, ..., Rn placed in series, the equivalent resistance Req is calculated simply by adding all the values:

Req = R1 + R2 + ... + Rn

The more resistors added in series, the more the total resistance increases: the current finds it increasingly difficult to flow.

Concrete example

Let R1 = 100 ohm and R2 = 220 ohm, connected in series.

Req = 100 + 220 = 320 ohm

If the circuit is powered by a voltage U = 6.4 V, the single current of the circuit is I = U / Req = 6.4 / 320 = 0.02 A, i.e. 20 mA.

Summary table

Quantity	In series
Current	Identical everywhere: I = I1 = I2 = ...
Total voltage	U = U1 + U2 + ... + Un
Equivalent resistance	Req = R1 + R2 + ... + Rn

Common pitfall

Don't confuse this law with that of the parallel arrangement (law of inverses, seen in the next chapter). In series, resistances are added directly: Req is always greater than the largest resistance in the circuit.