Ohm's law and power
Any two of V, I, R and P give the other two.
Try a job 4
Each job fills in example values. Replace them with your values.
- Find the resistance of a heater elementThe working resistance and current of a 2 kW heater on 230 V.
- Find the current of a 12 V lampThe current a 50 W lamp draws on 12 V d.c.
- Find the power of a three-phase heater bankThe kW of a star heater bank of 20 Ω per phase on 400 V.
- Find the voltage across a resistorThe volts across 470 Ω carrying 20 mA d.c.
Inputs
Worked example with the default inputs. The live calculator replaces it when the page loads.
- Supply
- Single-phase a.c.
- You know
- Voltage and power
- Voltage
- 230 V
- Real power
- 2,300 W
- Power factor
- 1
Current
10A
- Impedance
- 23Ω
- Apparent power
- 2.3kVA
This result is a design aid. Verify it against the current standard.
Calculation steps
- Formula
I = P ÷ (V × pf)
- Voltage230V
- CurrentResult10A
- Impedance23Ω
- Real power2,300W
- Apparent power2.3kVA
- Reactive power0kvar
- Resistance part, Z × pf23Ω
- Reactance part, Z × sin φ0Ω
About this calculator
How this is calculated
Ohm's law says the voltage across a resistance is the current through it times the resistance. The power formula says the power is the voltage times the current. Together they link four quantities, so any two of them give the other two. You pick the pair you know, and the tool solves for the rest.
On d.c. the four are voltage, current, resistance and power, and nothing else enters. On a.c. the current and voltage can be out of step, so two things change. The opposition to current is the impedance, Z, which the tool uses wherever d.c. uses R. The real power is the voltage times the current times the power factor. The tool then splits the impedance into its resistance part, Z times the power factor, and its reactance part, and gives the apparent and reactive power too.
On three phase the tool takes the line voltage, between two phases, and the line current. The real power is the square root of three times the line voltage times the line current times the power factor. The impedance it gives is one phase of a balanced star load: the voltage from line to neutral over the line current. A delta load with the same line current has three times that impedance in each branch.
No standard is read. These are the physics every electrician learns, and the tool shows the formula it used for the pair you gave.
| Step | Table or clause | What it decides |
|---|---|---|
| d.c. | V = I × R and P = V × I | The two unknowns from the pair you know |
| Single-phase a.c. | V = I × Z and P = V × I × pf | The current or voltage, the impedance and the real power |
| Three-phase a.c. | V = √3 × I × Z and P = √3 × V × I × pf | Line values and the impedance per phase of a star load |
| Power from resistance and current | P = I² × R | The power when the voltage is not given |
| The parts of the impedance | R = Z × pf and X = Z × sin φ | The resistance and reactance on a.c. |
Worked examples
- A 2 kW heater on 230 V draws 8.7 A. Its working resistance is 26.45 Ω.
- A 50 W lamp on 12 V d.c. draws 4.17 A through 2.88 Ω.
- A star heater bank of 20 Ω per phase on 400 V draws 11.55 A in each line and gives 8,000 W.
- A 470 Ω resistor carrying 20 mA has 9.4 V across it and gives off 0.188 W.
- A motor on 400 V drawing 32 A at 0.85 power factor looks like 7.22 Ω per phase and takes 18,844.71 W.
Limits
The tool treats every load as linear and balanced. It does not model harmonics, an unbalanced three-phase load or a load whose resistance changes with temperature, such as a lamp filament or a cold heater element. A meter reading on a cold element is lower than its working value.
For a cable's voltage drop, use the voltage drop tool: it reads the cable's resistance and reactance at its operating temperature from AS/NZS 3008.1.
See also: Three phase power, Full load current and Voltage drop.
Questions
Each answer describes what this tool calculates. The result is a design aid. Verify against the current standard.
What is Ohm's law?
The voltage across a resistance equals the current through it times the resistance: V = I × R. With P = V × I it links all four quantities, so any two give the other two.
How does power factor change the answer on a.c.?
On a.c. the opposition to current is the impedance Z, not only the resistance. Real power is V × I × power factor on one phase. The tool also gives the resistance part, Z × pf, and the reactance part.
How does the tool work three phase?
It takes the line voltage and line current. Real power is √3 × V × I × power factor. The impedance it gives is one phase of a balanced star load. A delta load has three times that in each branch.
Why does a heater element read a lower resistance cold?
A metal element's resistance rises with its temperature. A cold reading on a meter is lower than the working resistance. Use the rated volts and watts for the working value.
Can I use it for a cable's voltage drop?
Only roughly. A cable's resistance changes with temperature, and a.c. adds reactance. Use the voltage drop tool, which reads AS/NZS 3008.1 for the cable.
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