Ohm's law calculator: U, I, R and power P

Ohm's law: statement and detailed formulas

Formulated by Georg Simon Ohm in 1827, Ohm's law is the founding equation of linear electricity. It states that, in a metallic conductor at constant temperature, the current flowing through it is proportional to the voltage across its terminals, the proportionality coefficient being the inverse of the resistance.

The three equivalent forms are:

• U = R · I — voltage from resistance and current.
• I = U / R — current from voltage and resistance.
• R = U / I — resistance from voltage and current (voltmeter/ammeter method).

The dissipated power by Joule effect in the resistance is obtained through three equivalent forms:

• P = U · I — direct formulation in watts.
• P = R · I² — useful when R and I are known (shunts, LV lines).
• P = U² / R — useful when U and R are known (load resistance).

All these formulas assume consistent SI units: volts, amperes, ohms, watts. Multiplying mA by kΩ gives volts directly: it is the king of mnemonic tricks in signal electronics.

Table of common values

Ohm's law in AC vs DC: the nuance that changes everything

The most frequent confusion in the field: applying U = R · I in AC on any load. In direct current (DC), the resistance R is the only parameter opposing the current: the formula applies as is, with voltage and current as constant values.

In alternating current (AC), two cases arise. On a purely resistive load (heating resistor, incandescent lamp, conventional ceramic hob), Ohm's law remains valid in RMS values: U[V rms] = R · I[A rms]. On a reactive load (asynchronous motor, transformer, electromagnetic ballast, capacitor), the pure resistance R is replaced by theimpedance Z = √(R² + X²), with X_L = 2πfL or X_C = 1/(2πfC).

The major consequence concerns power. In reactive AC, three quantities are distinguished: the apparent power S = U · I [VA] which sizes cables and transformers, the active power P = U · I · cos φ [W] which corresponds to the energy actually converted, and the reactive power Q = U · I · sin φ [VAr] which circulates without useful work. NIBT 2020 requires a cos φ ≥ 0.9 on industrial feeders, failing which a compensation using capacitor banks must be provided for.

LED examples: series resistor and combinations

Single LED on a 12 V supply

Typical case of an LED signalling strip or a distribution board indicator. Take a white LED with forward voltage Vf = 3 V and rated current If = 20 mA on a 12 V DC supply. The limiting series resistor is:

R = (Vsupply − Vf) / If = (12 − 3) / 0,020 = 450 Ω

Choose the next higher standard value in the E12 series, i.e. 470 Ω (which slightly reduces the current to 19.1 mA, with no visible impact on brightness). The dissipated power is P = (Vsupply − Vf) · If = 9 · 0,020 = 0,18 W, i.e. a 1/4 W (0.25 W) package with a ×1.4 margin.

LEDs in series on 12 V

Three white LEDs at Vf = 3 V each in series drop 9 V, leaving 3 V for the resistor. With If = 20 mA: R = 3 / 0,020 = 150 Ω, standardized 150 Ω E12, dissipated power 60 mW (1/8 W is enough). This series arrangement triples the efficiency compared with three separate LEDs: 60 mW of losses instead of 540 mW, for the same total flux.

LEDs in parallel: avoid

Putting LEDs directly in parallel without a dedicated resistor for each creates a thermal imbalance: the hottest LED sees its Vf drop, draws more current, heats up further, until runaway (current hogging). The rule is to allocate one resistor per LED, calculated individually. For 4 parallel LEDs on 12 V: 4 × 470 Ω, total current 80 mA, total power 0.72 W spread across 4 resistors of 1/4 W.

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