Section 26.10 Resistors in Circuits: Series and Parallel
Subsubsection Key Ideas
When there is more than one resistor in a circuit, you can find the equivalent resistance using the rules of series and parallel resistors.
Principle 26.10.2. Combining Resistors in Series.
If \(N\) resistors are in series, the equivalent resistance is:
\begin{equation*}
R_{\mathrm{eq}} = \sum_{i = 1}^{N} R_i = R_1 + R_2 + R_3 + \dots
\end{equation*}
Principle 26.10.3. Combining Resistors in Parallel.
If \(N\) resistors are in parallel, the equivalent resistance is:
\begin{equation*}
\frac{1}{R_{\mathrm{eq}}} = \sum_{i = 1}^{N} \frac{1}{R_i} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots
\end{equation*}
Subsubsection Activities
Activity 26.10.1. Box of Resistors.
Suppose you have a box of identical resistors, each rated for 6 \(\Omega\text{.}\) Describe an arrangement of these resistors that has an equivalent total resistance of 4 \(\Omega\text{.}\)
