1. Let's start by defining **series circuits**. In a series circuit, components are connected end-to-end, so the same current flows through each component. 2. The total resistance $$R_{total}$$ in a series circuit is the sum of individual resistances: $$R_{total} = R_1 + R_2 + R_3 + \dots$$ 3. The total voltage $$V_{total}$$ across the series circuit is the sum of voltage drops across each component, following Kirchhoff's Voltage Law. 4. Next, a **parallel circuit** has components connected across the same two points, so the voltage across each component is the same. 5. The total resistance $$R_{total}$$ in a parallel circuit is found by: $$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots$$ 6. The total current $$I_{total}$$ entering a parallel circuit divides among the branches, according to Kirchhoff's Current Law. 7. A **series-parallel circuit** is a combination where some components are in series and others in parallel. 8. To analyze series-parallel circuits, identify simple series or parallel groups, reduce them step-by-step to find equivalent resistances, then apply series or parallel formulas as needed. 9. For example, if resistors $$R_1$$ and $$R_2$$ are in parallel, their equivalent resistance $$R_p$$ is: $$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}$$. Then if $$R_p$$ is in series with $$R_3$$, total resistance is $$R_{total} = R_p + R_3$$. Understanding these basics allows you to solve complex circuits by breaking them into simpler series and parallel parts.