Electric Circuits

Charge in Motion

A circuit is a closed loop through which charge flows. Three quantities describe it:

• Current $I$ — the rate of charge flow, in amperes (coulombs per second). Conventional current flows from high to low potential.
• Voltage $V$ — the potential difference driving the current, in volts (from the previous lesson).
• Resistance $R$ — how much a component opposes current flow, in ohms.

These are tied by Ohm's law, the single most-used equation in electronics: $$V = I R.$$ For a fixed resistance, more voltage drives more current; for a fixed voltage, more resistance means less current. Rearranged, $I = V/R$ — the current is the voltage divided by the resistance. The power dissipated (as heat) is $P = IV = I^2 R$, which is why resistors and chips get hot.

Components combine in two basic ways, with opposite rules:

• Series — components in a single line share the same current; their resistances add ($R = R_1 + R_2 + \dots$). Adding series resistance increases total resistance.
• Parallel — components across the same two nodes share the same voltage; the current splits among them, and the total resistance is less than any single branch (for two, $R = \frac{R_1 R_2}{R_1 + R_2}$). Adding parallel paths decreases total resistance.

This is the foundation of every electronic device. A processor is, at bottom, an astronomically complex circuit of transistors switching currents — and the same $V = IR$ and series/parallel reasoning analyzes both a flashlight and a chip's power delivery.

Common pitfall: swapping the series vs parallel resistance rules, or misapplying Ohm's law. In series, resistances add (total goes up); in parallel, the total is smaller than the smallest branch (adding paths lowers resistance) — reversing these is the classic mistake. And $V = IR$ must be rearranged carefully: current is $I = V/R$ (voltage over resistance), so more resistance means less current, not more.