Calculate the combined resistance of two or more resistors when they are connected in series.
Key Concepts
Series connection: Resistors are linked end‑to‑end so the same current flows through each resistor.
Combined (equivalent) resistance \$R_{\text{eq}}\$: The total resistance that a single resistor would have to produce the same effect as the series group.
Formula for Series Resistors
The combined resistance of \$n\$ resistors \$R1, R2, \dots , R_n\$ in series is the sum of their individual resistances:
\$\$
R{\text{eq}} = R1 + R2 + \dots + Rn
\$\$
Why the Sum?
In a series circuit the voltage across each resistor adds up to the total voltage supplied, while the current \$I\$ is the same through every resistor. Ohm’s law (\$V = IR\$) applied to each resistor and then to the whole circuit gives the additive rule.
Step‑by‑Step Procedure
Identify all resistors that are connected end‑to‑end with no branching points between them.
Write down the value of each resistor (in ohms, \$\Omega\$).
Apply the series formula: add the values together.
Record the result as the equivalent resistance \$R_{\text{eq}}\$.
Worked Example
Three resistors are connected in series: \$R1 = 4.7\;\Omega\$, \$R2 = 10\;\Omega\$, and \$R_3 = 15\;\Omega\$. Find the equivalent resistance.
Thus the series combination behaves like a single \$29.7\;\Omega\$ resistor.
Practice Table
Resistor Set
Values (Ω)
Combined Resistance \$R_{\text{eq}}\$ (Ω)
Set A
2.2, 3.3, 4.7
\$2.2 + 3.3 + 4.7 = 10.2\$
Set B
5, 5, 5, 5
\$5 \times 4 = 20\$
Set C
12, 8.2
\$12 + 8.2 = 20.2\$
Common Mistakes to Avoid
Adding resistances that are actually in parallel – check the circuit diagram carefully.
Confusing total voltage with total resistance; remember \$V{\text{total}} = I R{\text{eq}}\$.
Using incorrect units – keep all resistances in ohms before adding.
Summary
When resistors are connected in series, the current through each is identical and the total resistance is simply the arithmetic sum of the individual resistances. This principle allows us to replace a series network with a single equivalent resistor for analysis.
Practice Questions
Four resistors of \$2\;\Omega\$, \$3\;\Omega\$, \$5\;\Omega\$ and \$10\;\Omega\$ are connected in series. What is \$R_{\text{eq}}\$?
A circuit has a \$12\;\text{V}\$ battery and three series resistors: \$R1 = 1.5\;\Omega\$, \$R2 = 2.5\;\Omega\$, \$R_3 = 6\;\Omega\$. Calculate the current flowing through the circuit.
Explain why the voltage across each resistor in a series circuit is different if the resistors have different values.
Suggested diagram: A simple series circuit showing a battery, three resistors \$R1\$, \$R2\$, \$R_3\$ in line, and a current direction arrow.