Ohm’s Law Explained: Formula, Examples and an Interactive Circuit

Ohm’s law is usually the first equation anyone learns in electronics, and it’s one engineers still use dozens of times a day. This guide starts with intuition, lets you play with a live circuit, then works through the formulas, real circuits like LED resistors and voltage dividers, and the places where the law bends. Skip to whatever level suits you: the professional notes and practice problems are near the end.

What is Ohm’s law?

Ohm’s law says that the current flowing through a conductor is directly proportional to the voltage across it. The constant that links the two is the conductor’s resistance:

The law is named after the German physicist Georg Simon Ohm, who published it in 1827 in Die galvanische Kette, mathematisch bearbeitet after carefully measuring current through wires of different lengths and thicknesses. The symbol I comes from the French intensité du courant, which is why current isn’t written as C.

An intuition: water in a pipe

Electricity is invisible, so a picture helps. Imagine a water tank feeding a pipe:

• Voltage is the water pressure, set by how high the tank is.
• Current is the flow rate: litres per second, or coulombs per second in a wire.
• Resistance is the narrow section that limits flow.

The analogy breaks down eventually (water doesn’t need a return path, and electrons don’t pile up in a wire), but it’s good enough to build your intuition for everything on this page.

Try it: a live circuit

Move the sliders. The dots show charge moving around the loop: their speed follows the current. Watch what happens to the resistor when the power gets too high.

Voltage

9 V

Resistance

470 Ω

Current19.1 mA

Power in R172 mW

I = 9 V ÷ 470 Ω = 19.1 mA

Show electron flow

The Ohm’s law triangle

A quick memory aid: put V on top and I and R side by side underneath. Cover the quantity you want, and what’s left tells you the formula. Side by side means multiply; one above the other means divide.

Find V Find I Find R

V = I × R

Cover V: I and R sit side by side, so multiply them.

The three forms, with worked examples

Rearranging V = I × R gives the two other forms. They’re the same law, solved for a different unknown:

Power: why resistors get hot

Whenever current flows through a resistance, electrical energy turns into heat. The rate at which that happens is power, measured in watts:

The last two come from substituting Ohm’s law into P = V × I. Use whichever matches the values you already know.

All twelve relationships between V, I, R and P, for reference:

Reading a V–I graph

Plot current against voltage for a resistor and you get a straight line through the origin. That straight line is Ohm’s law: the slope is 1 ÷ R, so a steeper line means a smaller resistance. Components that follow this are called ohmic. Many useful parts don’t:

Resistor value

220 Ω

Resistor (ohmic) Filament lamp Silicon diode

At 6 V, the 220 Ω resistor passes 27.3 mA.

Ohm’s law in real circuits

1. Choosing an LED resistor

An LED isn’t ohmic: connected straight to a battery, it would draw as much current as the battery can supply and burn out. A series resistor sets the current. The resistor sees whatever voltage the LED doesn’t use:

R = (5 V − 2.0 V) ÷ 15 mA = 3 ÷ 0.015 = 200 Ω → nearest standard value 220 Ω

Check the real current with the value you chose: 3 V ÷ 220 Ω = 13.6 mA, comfortably bright and inside a typical 20 mA rating. The resistor dissipates 3 V × 13.6 mA ≈ 41 mW, so a ¼ W part is plenty. The forward voltage V_F depends on colour: roughly 1.8–2.2 V for red, and 2.8–3.3 V for blue and white. Always check the datasheet.

2. The voltage divider

Two resistors in series split a voltage in proportion to their values. It’s Ohm’s law applied twice: the same current flows through both, so each one’s voltage is that current times its resistance.

V_out = 5 × 20 kΩ ÷ (10 kΩ + 20 kΩ) = 3.33 V, with I = 5 V ÷ 30 kΩ = 0.17 mA through both

One catch: anything you connect to V_out draws current too and pulls the voltage down. Dividers are great for signals and sensing, but don’t power circuits from them.

3. Pull-up resistors

A microcontroller input needs a defined level when its button isn’t pressed, so a resistor “pulls” it up to the supply. When the button is pressed, the pin is shorted to ground, and Ohm’s law tells you what that costs:

I = 3.3 V ÷ 10 kΩ = 0.33 mA while the button is held

A 100 Ω pull-up would also “work”, but it would waste 33 mA every time the button is pressed, enough to drain a coin cell quickly. Values between 4.7 kΩ and 100 kΩ are typical. Lower values resist electrical noise better; higher values save power.

4. Measuring current with a shunt resistor

Turn Ohm’s law around and a resistor becomes a current sensor. Put a small, precise resistor in the current path and measure the voltage across it:

2 A through a 0.1 Ω shunt → V = 2 × 0.1 = 0.2 V to measure, and P = 2² × 0.1 = 0.4 W of heat

That’s how battery monitors, motor drivers and USB power meters measure current. Current-sense amplifiers such as the INA219 read that small voltage accurately. Note the trade-off: a bigger shunt gives a larger, easier-to-measure voltage but wastes more power.

Series and parallel resistors

When you combine resistors, Ohm’s law tells you how they behave together:

• Series: the same current flows through each resistor, and the voltages add up. Total resistance is the sum: two 1 kΩ resistors in series make 2 kΩ.
• Parallel: each resistor sees the same voltage, and the currents add up. Total resistance is always smaller than the smallest one. For two resistors, use “product over sum”: R = (R1 × R2) ÷ (R1 + R2). Two 1 kΩ resistors in parallel make 500 Ω.

Where Ohm’s law bends: notes for professionals

Ohm’s law is exact for an ideal resistor at constant temperature. Real designs live in the gaps:

Resistance changes with temperature

Copper’s temperature coefficient α is about 0.0039 per °C, so a copper trace that warms by 40 °C has about 16% more resistance. A tungsten lamp filament is far more extreme: cold, its resistance is roughly a tenth of its hot value, which is why bulbs draw a large inrush current at switch-on and usually fail at that moment.

Non-ohmic parts and dynamic resistance

Diodes, LEDs, transistors and thermistors don’t have a single resistance value. For small changes around an operating point, engineers use the dynamic (incremental) resistance, r = ΔV ÷ ΔI, which is the inverse slope of the V–I curve at that point. A diode’s dynamic resistance, for instance, falls as its current rises.

Wires and PCB traces are resistors too

R = 1.72×10⁻⁸ Ω·m × 0.1 m ÷ (0.25×10⁻³ m × 35×10⁻⁶ m) ≈ 0.2 Ω

At 2 A that trace drops 0.4 V and turns 0.8 W into heat. On a 3.3 V rail, 0.4 V is a 12% loss: enough to brown out a microcontroller under load. A handy figure for 1 oz copper is about 0.5 mΩ per square (a length equal to the width), so this trace is 400 squares ≈ 0.2 Ω. Widen power traces, use copper pours, and keep high-current paths short. It’s one of the first things we check in a PCB design review.

AC circuits: impedance

With alternating current, capacitors and inductors resist current in a frequency-dependent way. Ohm’s law still holds, with complex impedance Z in place of R: V = I × Z. For a pure resistor, Z = R and nothing changes.

The microscopic form

Inside a material, Ohm’s law is a local relationship between current density and electric field, J = σE, where σ is the conductivity. Integrate it over a uniform wire and you get back V = I × R with R = ρL ÷ A, the formula above.

Checking it with a multimeter

• Voltage: measure across a component (in parallel), with the circuit powered.
• Current: break the circuit and put the meter in series, with the probe in the A or mA socket. Never put a meter in current mode across a supply: it’s a near short circuit and will blow the meter’s fuse.
• Resistance: measure with the power off, ideally with one leg of the part lifted, because other components in the circuit form parallel paths and give you a lower reading.

Try it: measure the voltage across a resistor and the current through it, divide one by the other, and compare with the colour code. You’ve just verified Ohm’s law.

Common mistakes

1. Mixing units. 20 mA is 0.02 A, not 20 A. Convert first, or stick to the V–mA–kΩ shortcut.
2. Ignoring power rating. The right resistance at the wrong wattage still burns out.
3. Treating LEDs and diodes like resistors. They need a current-limiting resistor (or a constant-current driver).
4. Measuring resistance in a powered circuit. The reading is meaningless, and the meter can be damaged.
5. Forgetting tolerance. A 5% resistor marked 1 kΩ can be anywhere from 950 Ω to 1050 Ω. Design for the worst case.
6. Forgetting the wires. At high current, connectors, wires and traces have resistance that matters.

Quick reference

• V = I × R, I = V ÷ R, R = V ÷ I
• P = V × I = I² × R = V² ÷ R
• Series: R = R1 + R2 · Parallel: R = R1 × R2 ÷ (R1 + R2)
• Divider: V_out = V_in × R2 ÷ (R1 + R2)
• LED resistor: R = (V_supply − V_F) ÷ I_LED
• Choose resistor wattage ≥ 2 × the power it dissipates

Practice problems

Try each one before opening the answer.

Summary

• Ohm’s law, V = I × R, links voltage, current and resistance. Know any two and you can find the third.
• Power, P = V × I, tells you how much heat a part must handle.
• It’s exact for resistors, and the starting point for everything else: LEDs, dividers, sensors and PCB traces.
• Real parts drift with temperature, tolerance and frequency, so good designs leave margin.

Next in Basic Electronics, we’ll build on this with Kirchhoff’s laws, which explain how currents and voltages share out across a whole circuit. Questions or something unclear? Ask in the comments below and we’ll answer.

Frequently asked questions

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