Final answer:
Series circuits have components in a single pathway with the same current through each, resulting in a higher total resistance, while parallel circuits have multiple pathways where the same voltage is applied across each component, leading to a lower total resistance than any individual one.
Step-by-step explanation:
The main difference between series and parallel circuits is how components, such as resistors, are connected and how current flows through them. In a series circuit, components are connected end-to-end in a single pathway, so the same current flows through each component. By contrast, a parallel circuit has components connected across common points, providing multiple pathways; this means each component has the same voltage across it, but the current can vary in each pathway depending on the resistance.
Concerning resistance, series circuits have a total resistance that is the sum of individual resistances, which results in a higher overall resistance and therefore, less current flow for the same voltage, compared to parallel circuits. For parallel circuits, the total resistance is less than the smallest individual resistance because the current has multiple paths to take, leading to a higher total current flow for the same voltage. This explains why appliances are commonly connected in parallel, as it allows them to operate independently and safely at the required voltage and current levels.
When analyzing a circuit, to calculate the equivalent resistance, different formulas are applied based on whether resistors are connected in series or parallel. In series, resistances are added algebraically (R_eq = R1 + R2 ...). In parallel, the reciprocal of the total resistance is the sum of the reciprocals of each resistor's resistance (1/R_eq = 1/R1 + 1/R2 ...).