2 Circuit Fundamentals

Circuit diagrams and connectivity

A circuit diagram, also called a schematic, uses standardized symbols and lines to show how components are electrically connected. It represents connectivity, not the physical shape or placement of wires. A wire joins points into the same electrical node, and a junction dot indicates a connection. Lines that cross without a dot are often shown as unconnected, although conventions can vary.

Common schematic symbols include a voltage source, resistor, and switch. In the example below, the source and two resistors form one path; the simplified resistor boxes show components, while the important feature is the single route for current before it returns to the source.

Series and parallel connections

Components in a series connection are connected end-to-end in one path, with no branching between them. The same current passes through every component, and their voltage drops add. For resistors in series, the equivalent resistance is the sum:

For example, resistors of $2\ \Omega$ and $3\ \Omega$ in series have an equivalent resistance of $5\ \Omega$.

Components in a parallel connection have both ends connected to the same two nodes. Each branch has the same voltage across it, while current divides among the branches. The reciprocal resistances add:

For two parallel resistors, the equivalent resistance can also be calculated as

For example, resistors of $6\ \Omega$ and $3\ \Omega$ in parallel have an equivalent resistance of $2\ \Omega$. A parallel equivalent is always less than the smallest individual resistance because the added branch provides another path for current.

Open and short circuits

An open circuit has a break in its conducting path, so no current can flow across the break. An open switch creates an open circuit. In a series path, an opening anywhere stops current throughout that path. In a parallel circuit, an open branch stops current in that branch, while other complete branches may still conduct.

A short circuit is an unintended, very-low-resistance connection that bypasses some or all of a component. For example, a wire directly across a lamp can divert current around it, so the lamp may not light. A short across a voltage source can draw dangerously high current, causing overheating or damage. Real current is limited by the source and wiring, but should not be assumed safe.

Finding equivalent resistance

Equivalent resistance is the resistance of one resistor that could replace a resistor network while producing the same overall voltage–current relationship at its terminals.

To simplify a series-parallel circuit:

1. Identify a group whose resistors are clearly in series or clearly in parallel.

2. Replace that group with its equivalent resistance.

3. Redraw the simplified circuit and repeat until one resistance remains.

For example, a $4\ \Omega$ resistor in series with a parallel pair of $6\ \Omega$ and $3\ \Omega$ has an equivalent resistance of

These reduction rules apply only when the connections truly meet the definitions of series or parallel. A circuit that cannot be divided into such groups may require other circuit-analysis methods.