Every circuit analysis begins with three numbers and one equation: V = I × R. Georg Ohm published this relationship in 1827, and nearly two centuries later it remains the single most-used equation in electrical work — from sizing a residential branch circuit to troubleshooting a 480V industrial distribution panel. Voltage (V) drives current (I) through resistance (R), and the power dissipated (P = V × I) determines conductor heating, equipment ratings, and energy consumption. Mastering these four variables and their twelve derivative formulas (the 'power wheel') is the foundation every electrician and engineer builds upon.

The power wheel expands Ohm's Law into twelve equations by combining V = IR with P = VI: P = I²R, P = V²/R, I = P/V, I = √(P/R), R = V²/P, R = P/I², V = P/I, V = √(P×R). Given any two known quantities, the other two can be calculated. In the field, the most common application is determining current from known power and voltage: a 1,500W space heater on a 120V circuit draws I = P/V = 12.5A — confirming it fits on a 15A circuit with 80% continuous load margin (12A limit for continuous).

Series circuits add resistances (R_total = R₁ + R₂ + R₃) — current is equal through all components while voltage divides proportionally. Parallel circuits add conductances (1/R_total = 1/R₁ + 1/R₂) — voltage is equal across all branches while current divides. In practical wiring, branch circuits are parallel loads on a panel bus: each receptacle sees full 120V regardless of other loads. However, the conductors supplying the panel are in series with those loads — their resistance causes voltage drop that increases with total current draw.

Temperature profoundly affects resistance — and therefore every Ohm's Law calculation in real installations. Copper has a temperature coefficient of +0.00393 per °C, meaning its resistance increases approximately 0.4% per degree above 20°C. At 75°C (conductor operating temperature), copper resistance is about 22% higher than at 20°C (reference temperature). This is why NEC Table 8 lists DC resistance at 75°C for conductor sizing, while measured cold resistance of new installations will always be lower. Aluminum has a coefficient of +0.00403 — slightly higher than copper.

In AC circuits, Ohm's Law applies using impedance (Z) rather than pure resistance (R). Impedance includes both the resistive component (R) and the reactive component (X — inductive or capacitive reactance): Z = √(R² + X²). For purely resistive loads — electric heaters, incandescent lamps — R and Z are identical, and Ohm's Law V = IR works directly with RMS values. For motors, transformers, and electronic power supplies, the inductive reactance causes current to lag voltage, reducing the power factor and requiring the full impedance calculation.

Kirchhoff's laws extend Ohm's Law to complex circuits: Kirchhoff's Current Law (KCL) states that currents entering a node must equal currents leaving (conservation of charge). Kirchhoff's Voltage Law (KVL) states that the sum of voltages around any closed loop must equal zero (conservation of energy). These laws, combined with Ohm's Law, enable analysis of any circuit — from a simple residential panel with multiple branch circuits to a complex industrial power distribution network with multiple sources and interconnections.