Compare series and parallel circuits: in series the current is the same and voltage divides; in parallel the voltage is the same and current divides, and adding parallel branches lowers the total resistance (MA STE Introductory Physics, electric circuits).

What this topic is asking

The Massachusetts Introductory Physics MCAS expects you to compare the two ways of connecting components. You must describe a series circuit (one path: the current is the same everywhere, and the voltage divides among the components) and a parallel circuit (multiple branches: the voltage is the same across each branch, the current divides, and adding branches lowers the total resistance). The crosscutting idea is systems and system models: how components are connected changes how current and voltage are shared.

Series circuits

The defining feature is the single path, and from it the MCAS draws several rules:

• Current is the same everywhere. Whatever current leaves the battery passes through each component in turn.
• Voltage divides. The battery voltage is split across the components; the voltage drops across them add up to the battery voltage.
• Total resistance adds up. More components in series means more total resistance, which (by Ohm's law) means a smaller current, so series bulbs are dimmer the more you add.
• One break stops everything. Because there is one path, a single broken component (or a gap) stops the current through the whole circuit. Old holiday lights where one dead bulb killed the whole string are the classic example.

Parallel circuits

Parallel is the opposite pattern, and again the rules follow from the structure:

• Voltage is the same across each branch. Every branch gets the full battery voltage, so parallel bulbs all shine at full brightness.
• Current divides. The total current from the battery splits among the branches and recombines; branches with less resistance carry more current.
• Total resistance drops. Adding more parallel branches gives the current more paths, so the total resistance decreases and the total current from the battery increases.
• Branches are independent. If one branch breaks, the others keep working, because each has its own path. This is why removing one bulb does not darken the rest.

Why homes are wired in parallel

This is a favorite MCAS application. In a parallel home circuit, the toaster, the lights, and the television each sit on their own branch at the full mains voltage, so each works at its rated power and any one can be turned off without affecting the others. The same independence that keeps one bulb lit when another is removed is what makes parallel wiring practical for buildings.

Worked example

Reference-sheet note

The reference sheet gives Ohm's law $V = IR$ and electrical power $P = IV$, which you apply within a circuit, but it leaves the series and parallel rules blank for you to recall. What you recall is: series means one path, same current, voltage divides, resistance adds, one break stops all; parallel means separate branches, same voltage, current divides, resistance drops, branches independent; and that homes are wired in parallel.

Try this

Q1. In a series circuit, state how the current through each component compares. [1]

• Cue. The current is the same through every component (there is a single path).

Q2. In a parallel circuit, state how the voltage across each branch compares to the battery voltage, and what happens to the others if one branch breaks. [2]

• Cue. Each branch has the full battery voltage; if one branch breaks, the others keep working because each is an independent path.