Ohm's Law is the most useful equation in electrical work. It links the three basic quantities of a circuit (voltage, current and resistance), so if you know any two, you can calculate the third. Electricians use it to check circuits, electronics hobbyists use it to choose resistors, and engineers use it every day in design and fault-finding.
In this guide you will learn the formula, the easy triangle method, five fully worked examples, how Ohm's Law combines with power, and the important cases where it does not apply directly.
What is Ohm's Law?
Ohm's Law states that the current through a conductor is directly proportional to the voltage across it, provided its temperature and other physical conditions stay the same. The constant that links them is the resistance.
| Symbol | Quantity | Unit |
|---|---|---|
| V | Voltage (potential difference) | volt (V) |
| I | Current | ampere (A) |
| R | Resistance | ohm (Ω) |
The law is named after the German physicist Georg Simon Ohm, who published his findings in 1827. The unit of resistance, the ohm, is also named after him.
The three forms of the formula
Rearranging V = I × R gives three versions, one for each unknown:
| To find | Use | In words |
|---|---|---|
| Voltage | V = I × R | Multiply current by resistance |
| Current | I = V ÷ R | Divide voltage by resistance |
| Resistance | R = V ÷ I | Divide voltage by current |
The Ohm's Law triangle (easy memory trick)
Draw a triangle with V on top and I × R on the bottom. Cover the quantity you want to find:
- Cover V → you see I and R side by side → V = I × R
- Cover I → you see V over R → I = V ÷ R
- Cover R → you see V over I → R = V ÷ I
The graph shows the same law visually. For a fixed resistor, current rises in a straight line as voltage rises. The 10 Ω line is twice as steep as the 20 Ω line, because a lower resistance lets more current flow at the same voltage.
Worked examples
Example 1: Find the current (heater element)
A heating element has a resistance of 46 Ω and is connected to 230 V. What current flows?
The element draws 5 A. (Its power is 230 × 5 = 1150 W. See the power section below.)
Example 2: Find the voltage
A current of 2 A flows through a 6 Ω resistor. What is the voltage across it?
Example 3: Find the resistance (and a lesson about lamps)
A 12 V filament lamp draws 0.5 A when lit. What is its resistance?
This is the lamp's hot resistance. If you measure the cold lamp with a multimeter, you will read much lower, because a metal filament's resistance rises a lot as it heats up. That is why a filament lamp draws a short surge of current when first switched on.
Example 4: Working with milliamps and kilohms
A 5 V supply is connected across a 1 kΩ resistor. What current flows?
Useful shortcut: volts ÷ kilohms = milliamps. So 5 V ÷ 1 kΩ = 5 mA directly.
| Prefix | Meaning | Example |
|---|---|---|
| m (milli) | × 0.001 | 20 mA = 0.02 A |
| µ (micro) | × 0.000001 | 50 µA = 0.00005 A |
| k (kilo) | × 1000 | 4.7 kΩ = 4700 Ω |
| M (mega) | × 1,000,000 | 1 MΩ = 1,000,000 Ω |
Example 5: Choosing a resistor for an LED
You want to run a red LED from a 5 V supply (for example an Arduino pin). The LED datasheet gives a forward voltage of about 2 V, and you want about 15 mA. The resistor must drop the remaining voltage:
200 Ω is not a common value in the E12 series, so choose the next higher standard value, 220 Ω. The actual current is then (5 − 2) ÷ 220 ≈ 13.6 mA, which is safe and still bright. Resistor power: 0.0136² × 220 ≈ 0.04 W, so a standard 0.25 W resistor is fine.
Ohm's Law and power
Power is P = V × I. By substituting Ohm's Law into it, you get two more useful forms. Together they let you find any of V, I, R or P from any two others:
| You know | Find current | Find power |
|---|---|---|
| V and R | I = V ÷ R | P = V² ÷ R |
| I and R | (given) | P = I² × R |
| V and I | (given) | P = V × I |
| P and V | I = P ÷ V | (given) |
Example: a 1 kW heater on 230 V draws I = 1000 ÷ 230 ≈ 4.35 A, and its element resistance is R = 230² ÷ 1000 ≈ 52.9 Ω (when hot).
Why it matters for resistors: the P = I² × R form tells you how much heat a resistor must handle. Always choose a resistor with a power rating comfortably above the calculated value.
Practical use: voltage drop in a cable
Cables have resistance too. A 10 m run of 1.5 mm² copper cable has roughly 0.23 Ω in total for line and neutral together (at 20 °C). At a load current of 10 A:
So the load receives about 2.3 V less than the supply. On long runs or high currents, this drop can make motors run hot and lights dim, which is why voltage drop is checked during cable selection. Real installations must follow the cable tables and voltage-drop limits in your local wiring regulations.
When Ohm's Law does not apply directly
V = I × R with a single fixed R works for ohmic components such as ordinary resistors and metal wires at a steady temperature. Be careful with these cases:
| Component or situation | Why a simple fixed R does not work |
|---|---|
| Diodes and LEDs | Current rises very steeply once the forward voltage is reached; the V–I curve is not a straight line |
| Filament lamps | Resistance increases strongly with temperature |
| Thermistors and LDRs | Resistance changes with temperature or light by design |
| AC circuits with motors, coils or capacitors | Opposition to current is impedance (Z), which includes reactance; use V = I × Z |
| Motors while running | Back-EMF reduces current as speed rises; winding resistance alone does not predict running current |
Checking Ohm's Law with a multimeter
- Take a resistor (for example 1 kΩ) and measure its resistance with the circuit disconnected.
- Connect it to a low-voltage DC supply, such as a 9 V battery.
- Measure the voltage across the resistor (meter in parallel).
- Measure the current with the meter in series on the mA range.
- Check that V ÷ I is close to the measured resistance. Small differences come from meter accuracy and resistor tolerance.
Common mistakes
- Forgetting to convert mA to A or kΩ to Ω before calculating.
- Using cold (measured) resistance to calculate the current of a lamp, heater or motor.
- Using V ÷ R for AC motor circuits instead of using nameplate current or impedance.
- Choosing a resistor value but forgetting to check its power rating.
- Measuring resistance while the circuit is still powered.
Practice questions
- A 24 V supply is connected across a 12 Ω resistor. Find the current.
- A 0.25 A current flows through a 100 Ω resistor. Find the voltage across it.
- A device draws 3 A from a 12 V battery. What is its effective resistance?
- What power is dissipated in a 470 Ω resistor carrying 20 mA?
Show answers
- I = 24 ÷ 12 = 2 A
- V = 0.25 × 100 = 25 V
- R = 12 ÷ 3 = 4 Ω
- P = 0.02² × 470 = 0.188 W (use at least a 0.25 W resistor, preferably 0.5 W for margin)
Frequently asked questions
Is Ohm's Law true for all materials?
No. It applies to ohmic conductors at constant temperature. Semiconductors, gas discharge lamps and many other devices are non-ohmic.
Does Ohm's Law work for AC?
Yes for purely resistive AC loads such as heaters, using RMS values. For circuits with inductance or capacitance, use impedance: V = I × Z.
Why is it called "Ohm's" Law?
It is named after Georg Simon Ohm, who published the relationship in 1827.
What is the difference between Ohm's Law and the power formula?
Ohm's Law links V, I and R. The power formula P = V × I tells you the rate of energy use. Combining them gives P = I² × R and P = V² ÷ R.
What to read next
- Voltage, Current, Resistance and Power Explained
- AC vs DC: Differences, Waveforms, Uses and Safety
- Series and Parallel Circuits (coming soon)
References
- BIPM, The International System of Units (SI Brochure), for the volt, ampere and ohm.
- IEC 60050 (International Electrotechnical Vocabulary), electropedia.org.
- IEC 60063, Preferred number series for resistors and capacitors (E-series values such as E12).
Technical note: worked examples use rounded values for learning. Component values and ratings must come from the manufacturer's datasheet, and installation work must follow your local electrical code.
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