FundamentalsPower & Energy

Ohm’s law, electrical power and energy

Connect voltage, current, resistance, power, and energy; convert units; and check your results with DC circuit examples.

Level

Beginner

Reading time

12 min

Primary standard or source

IEC 80000-6 and BIPM — The SI Brochure

Last verified

13 September 2026

Associated tool

Ohm’s law calculator

Written and technically reviewed byElectroDesignForge Engineering Team

View the editorial process

Key point: in a resistive DC circuit, Ohm’s law connects voltage V, current I, and resistance R. Power P is the rate of energy transfer; energy E also depends on time.

Quick reference

The equations below assume a resistive DC load, or RMS values in AC. Reactive loads, switch-mode converters, and non-sinusoidal signals require additional consideration of power factor and waveform.

Ohm’s law: V, I, and R relationships

V = I × R
I = V / R
R = V / I

At a fixed resistance, a higher voltage produces more current. At a fixed voltage, a higher resistance limits current.

Electrical power: P, V, I, and R relationships

Power describes how quickly a load receives or dissipates energy.

P = V × I
P = I² × R
P = V² / R

When selecting a resistor, compare its rated power to calculated dissipation. A common practical starting margin is at least ×2, then check the manufacturer’s temperature derating curve.

Electrical energy: P, E, and time

Power alone does not state how much energy was used; it must be multiplied by duration.

E = P × t
P = E / t
t = E / P

In SI units, 1 W = 1 J/s, therefore E (J) = P (W) × t (s).

For batteries and electricity use, watt-hours are more convenient:

E (Wh) = P (W) × t (h)
1 Wh = 3,600 J
1 kWh = 1,000 Wh = 3.6 MJ

Useful conversions

Ampere-hours (Ah) quantify charge. To compare batteries with different voltages, compare watt-hours: Wh ≈ nominal V × Ah.

Worked examples

1. A resistor supplied from 12 V

A 120 Ω resistor is supplied from 12 V.

I = V / R = 12 / 120 = 0.1 A = 100 mA
P = V × I = 12 × 0.1 = 1.2 W

The resistor dissipates 1.2 W. A 1 W resistor is not adequate; choose a higher rating, such as 3 W in ordinary thermal conditions, after checking its derating curve.

2. LED with a series resistor

An LED has a 2 V forward voltage and needs 20 mA from a 5 V supply.

V_R = 5 − 2 = 3 V
R = V_R / I = 3 / 0.02 = 150 Ω
P_R = V_R × I = 3 × 0.02 = 0.06 W = 60 mW

A 150 Ω, 0.125 W resistor meets the power requirement; a 0.25 W part leaves more margin. Always check supply tolerance and the LED’s forward-voltage range.

3. Energy used by equipment

Equipment consumes 18 W for 8 h.

E = P × t = 18 × 8 = 144 Wh = 0.144 kWh

This is the billable or battery-supplied energy before converter losses and autonomy margin.

Verification method

1. Work in base units: V, A, Ω, W, and s or h.
2. Choose two independent quantities for Ohm’s law; the third follows.
3. Calculate power in every component that can heat.
4. Multiply power by time to find energy.
5. Sanity-check the magnitude and apply each component’s voltage, current, and temperature limits.

Limits and safety

• Ohm’s law alone does not model diodes, transistors, filament lamps, or converters: their effective resistance can change with voltage, current, or temperature.
• P = V × I applies to DC. In AC, active power also depends on power factor: P = V_RMS × I_RMS × cos φ for a sine wave.
• A low calculated power does not make a circuit safe. Mains voltage or a battery able to supply high current requires suitable protection and procedures.

Associated tool

Open the Ohm’s law calculator to solve V, I, R, and P from two values, with a resistor-power and fuse-rating recommendation.

Sources

• IEC 80000-6 — Quantities and units: electromagnetism.
• BIPM — The International System of Units (SI Brochure).
• IEC 60364-1 — Low-voltage electrical installations: fundamental principles and safety.