Ohm's Law Explained

Voltage, current and resistance are the three quantities that underpin almost every electrical calculation. Ohm's Law ties them together in one simple relationship -- and once you truly understand it, a huge portion of practical electronics becomes straightforward.

What Is Ohm's Law?

Ohm's Law states that the voltage across a conductor is directly proportional to the current flowing through it, provided temperature and other physical conditions remain constant. In equation form:

The law is named after the German physicist Georg Simon Ohm, who published the relationship in 1827. It is not a universal law of nature in the strictest sense -- some components, such as diodes and thermistors, do not obey it -- but it holds accurately for metallic conductors over a wide range of conditions and is the foundation of circuit analysis.

The Three Forms of the Formula

Because the equation has three variables, you can rearrange it to solve for whichever one is unknown:

A handy memory aid is the Ohm's Law triangle: write V at the top, I and R side by side at the bottom. Cover the quantity you want to find and the remaining two show you the operation -- side by side means multiply, one above the other means divide.

You can work through these calculations instantly with the Ohm's law calculator, which solves for any of the three variables and handles both DC and AC (single-phase) circuits.

Worked Examples

Example 1: Finding current through a resistor

A 12 V battery is connected across a 470 Ω resistor. What current flows?

Using I = V ÷ R:   I = 12 ÷ 470 = 0.0255 A (25.5 mA)

Example 2: Finding the voltage drop

A cable carries 8 A and has a resistance of 0.35 Ω. What is the voltage drop along the cable?

Using V = I × R:   V = 8 × 0.35 = 2.8 V

This is exactly how voltage drop calculators work under the hood -- the cable resistance is a function of conductor material, cross-sectional area and length, and the resulting voltage drop is simply I × R.

Example 3: Finding an unknown resistance

A component draws 150 mA from a 5 V supply. What is its resistance?

Using R = V ÷ I:   R = 5 ÷ 0.15 = 33.3 Ω

Ohm's Law and Resistor Selection

One of the most practical applications of Ohm's Law in everyday electronics is choosing a current-limiting resistor for an LED. LEDs are not ohmic devices -- they have a forward voltage drop (typically 1.8 V to 3.5 V depending on colour) and will draw as much current as the circuit allows if unprotected, burning out almost immediately.

The approach is to subtract the LED's forward voltage from the supply voltage to find the voltage across the resistor, then apply Ohm's Law:

Use the LED resistor calculator to find the correct resistor value for any LED and supply voltage combination. Once you have a value, check the colour bands on your component with the resistor colour code calculator to confirm you have the right part.

Series and Parallel Circuits

Series circuits

When resistors are connected end to end (in series), the total resistance is simply their sum: R_total = R₁ + R₂ + R₃ + ... The same current flows through each component, and the voltage divides across them in proportion to their individual resistances. This is Ohm's Law applied to each element in turn.

Parallel circuits

When resistors share the same two nodes (in parallel), the voltage across each is identical, but the current divides. The total resistance is found from the reciprocal rule: 1/R_total = 1/R₁ + 1/R₂ + ... Parallel combinations always produce a total resistance lower than the smallest individual resistor.

In domestic wiring, all the circuits in a consumer unit are wired in parallel from the main supply -- each circuit sees the full mains voltage (230 V in the UK, 120 V in North America) regardless of how many others are running. The current drawn from the supply is the sum of all branch currents.

Power and Ohm's Law

Ohm's Law pairs closely with the power formula P = V × I. Substituting the Ohm's Law expressions gives two further useful variants:

• P = I² × R -- useful when you know current and resistance (e.g. calculating cable heat losses)
• P = V² ÷ R -- useful when you know voltage and resistance (e.g. power dissipated in a fixed resistive load)

These forms are essential for checking that a resistor's power rating (commonly 0.25 W or 0.5 W for through-hole types) is not exceeded. In the LED example above, the 150 Ω resistor dissipates P = (0.020)² × 150 = 0.060 W (60 mW), well within a standard 0.25 W rating.

Where Ohm's Law Does Not Apply

Ohm's Law describes linear (ohmic) resistors, where V and I are proportional. Several common components behave non-linearly:

• Diodes and LEDs -- current rises exponentially once forward voltage is exceeded, which is why a current-limiting resistor is always needed.
• Thermistors (NTC/PTC) -- resistance changes significantly with temperature, so the relationship between V and I shifts as the device warms up.
• Incandescent bulbs -- the tungsten filament has a much higher resistance when hot than when cold; cold inrush current can be ten or more times the running current.
• Inductors and capacitors -- in AC circuits, these components introduce reactance, which is frequency-dependent and phase-shifted. Ohm's Law extends to AC via impedance Z, but the simple DC form no longer applies directly.

Understanding these exceptions is as important as knowing the law itself -- applying V = IR blindly to a diode, for instance, will give a nonsensical result.

Frequently Asked Questions