Ohm’s law and electrical power, explained.
Voltage provides an electrical potential difference. Current through an ohmic resistor is voltage divided by resistance. Electrical power is energy transferred per unit time: P = VI = V²/R.
The relationship to remember
Key formulas
- Ohm’s law
- V = IR
- Voltage = current × resistance
- Current
- I = V/R
- Amperes from volts and ohms
- Resistance
- R = V/I
- Ohms from a measurement
- Power
- P = VI
- Watts = volts × amperes
- Power from current
- P = I²R
- Substitute V = IR
- Power from voltage
- P = V²/R
- Substitute I = V/R
Worked example
Problem. A 9 V battery is connected across a 450 Ω resistor. Find the current and the power, and check the power with all three formulas.
- Current: I = V/R = 9 / 450 = 0.02 A (20 mA).
- Power: P = VI = 9 × 0.02 = 0.18 W.
- Check: P = I²R = 0.02² × 450 = 0.18 W, and P = V²/R = 81 / 450 = 0.18 W.
Answer. The resistor carries 0.02 A and dissipates 0.18 W.
A quick check
With 12 V across 100 Ω, current is 0.12 A and power is 1.44 W.
Inside the default experiment
- I = V/R = 12/100 = 0.12 A.
- P = VI = 12 × 0.12 = 1.44 W.
When this model applies
Ideal DC voltage source and an ohmic resistor with constant resistance; wires have zero resistance.
Make a prediction. Then test it.
Double the voltage. What happens to current? What happens to power?
Try it: Ohm’s law & power calculator ↗Frequently asked questions
Wondering about the why? Start here.
What happens when resistance increases?
At fixed voltage, current decreases because I = V/R. Power also decreases as V²/R.
Why is zero resistance not allowed?
An ideal source connected across zero resistance would demand an unbounded current. Real circuits have internal resistance and other limits.