11.3 Resistors in Electric Circuits

If components are in one unbranched path, charge that enters one component must pass through the next in the same amount per second, so current is common. Voltage drops then add to source rise. Increasing the number of series resistors increases total resistance and therefore reduces loop current for fixed emf.

Series design is common when you want to limit current or partition source voltage. However, high series resistance can starve power-hungry loads, so design choices depend on whether current control or power delivery is the priority.

Parallel branches share the same two nodes, so each branch sees the same potential difference. Branch currents then depend on branch resistances. Lower resistance branch takes larger current. Adding a new parallel branch increases total current demand from source because equivalent resistance decreases.

This is why domestic circuits distribute appliances in parallel: each device gets full supply voltage while drawing its own current. A fault in one branch does not remove supply from every other branch, unlike a strict series chain.

These rules are not separate laws from mechanics; they are direct applications of conservation principles in circuit form. The junction rule prevents charge accumulation at ideal nodes in steady state. The loop rule ensures that energy gained from sources equals energy lost across passive elements around a closed path.

For exam networks, first collapse obvious local series and local parallel groups, then redraw the circuit after each reduction step. Never collapse components that are only visually nearby; collapse only by topology. Re-drawing after each step prevents accidental misclassification and keeps current paths explicit.

After equivalent resistance and total current are found, back-substitute from outer loop inward to recover branch currents and individual voltage drops. This reverse pass is where marks are often won in multi-part questions.