Resistors in Series

Description how to calculate resistors in series

Resistors in Series

When multiple resistors are connected in a line where the current flows through them in sequence, we call it a series connection of resistors.

Total resistance

The total resistance results from the addition of the individual resistors

\(R_{ges} = R_1+R_2+R3\)


The flowing current through the individual resistors is equal and corresponds to the total current of the circuit.

\(\displaystyle I=\frac{U}{R_{ges}}\)


The total voltage across the total resistance is the sum of the individual voltages at the individual resistors


The applied total voltage is divided by the individual resistances in proportion to their values.

\(\displaystyle \frac{U_{ges}}{R_{ges}}=\frac{U_1}{R_1}=\frac{U_2}{R_2}=\frac{U_3}{R_3}\)

From this, the formula for a single voltage can be derived.

\(\displaystyle U_1=\frac{R_1·U_{ges}}{R_{ges}}\)


We calculate the total resistance, the current and the individual voltages at the resistors. The total voltage is given with \(230\) Volt.

\(\displaystyle R_{ges}=R_1+R_2+R_3=20+40+55=115Ω\)
\(\displaystyle I=\frac{U}{R_{ges}}=\frac{230}{115}=2A\)
\(\displaystyle U_1=R_1·I=20·2=40V\)

\(\displaystyle U_1=\frac{R_1·U_{ges}}{R_{ges}}=\frac{20·230}{115}=40V\)
\(\displaystyle U_2=R_2·I=40·2=80V\)

\(\displaystyle U_2=\frac{R_2·U_{ges}}{R_{ges}}=\frac{40·230}{115}=80V\)
\(\displaystyle U_3=R_3·I=55·2=110V\)

\(\displaystyle U_3=\frac{R_3·U_{ges}}{R_{ges}}=\frac{55·230}{115}=110V\)