Resistors in Series

Two resistors are in series when they are connected one after the other along the same wire, with no branching in between: the current has no alternative and must pass through both. Hence the key property: the current $i$ is the same in every resistor of the chain.

Two resistors in series: the same current $i$ flows through $R_1$ and $R_2$.

Since each resistor accounts for part of the source’s voltage, and the drops occur one after another along the path, the voltages add up: $\Delta V = \Delta V_1 + \Delta V_2 + \cdots = R_1 i + R_2 i + \cdots$

Factoring out the common current $i$ immediately gives the equivalent resistance of the chain.

Principle — Resistors in series

Same current through all resistors; voltages add up.

Key formula

$\ev{R_\text{eq} = R_1 + R_2 + R_3 + \cdots}$

Adding resistors in series always increases the total resistance: it lengthens the path the current must overcome.

Summary

In series the current is the same and the resistances add up. Two equal resistors $R$ give $R_\text{eq} = 2R$.

Links

Topics: Circuiti elettrici Concepts: Resistenze in serie e parallelo

Related exercises: Esercizio svolto — rete mista serie e parallelo · Problema — vero o falso su serie e parallelo · Problema — resistenza equivalente serie-parallelo