Library / Electrical / ELE-04
Electrical
Ohm’s law
Voltage across a resistor from the current through it and its resistance.
- Ref
- ELE-04
- Rev
- v1
- Field
- Electrical
- Result
- V [V]
V in volts, I in amperes, R in ohms. Rearranged: I = V/R and R = V/I.
For a resistor at a steady temperature, the voltage across it is proportional to the current through it. The constant of proportionality is the resistance.
Calculator
- Power I²R6 W
- Conductance 1/R0.04167 S
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The relation is linear: doubling the current doubles the voltage across the same resistor. The sweep chart over current is a straight line through the origin.
- Because V is a product, a 10% change in either input gives a 10% change in V. The driver ranking mostly reflects how wide each typical range is.
- Use Solve for I to find the current a given voltage drives through a given resistor, or Solve for R to find a resistance from a measurement.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (V) | Local step | Change in result |
|---|---|---|---|---|---|---|
| R Resistance | 1 to 1,000 Ω | 0.5 | 500 | 499.5 | +10% | +10 % |
| I Current | 0.01 to 10 A | 0.24 | 240 | 239.8 | +10% | +10 % |
Sweep of Current
| Current (A) | Voltage across the resistor (V) |
|---|---|
| 0.01 | 0.24 |
| 0.02371 | 0.5691 |
| 0.05623 | 1.35 |
| 0.1334 | 3.2 |
| 0.3162 | 7.589 |
| 0.7499 | 18 |
| 1.778 | 42.68 |
| 4.217 | 101.2 |
| 10 | 240 |
Sweep one variable
Variables and how each one contributes
Voltage across the resistor
What the equation gives you. Everything else feeds it.
Current
Current through the resistor. Voltage rises in proportion to current when R is fixed.
Resistance
Opposition of the resistor to current flow. Voltage rises in proportion to R at a fixed current. In a series circuit the largest resistance takes the largest share of the voltage.
Worked example with the values above
- Check the units: ampere × ohm = volt.
- V = IR = 0.5 A × 24 Ω = 12 V.
Assumptions and limits
- Ohmic conductor: R does not change with voltage or current.
- Constant temperature. Heating changes R (see resistance and temperature).
- Direct current, or AC with a purely resistive load (RMS values).
Common mistakes
- Applying V = IR to non-ohmic devices such as diodes and lamp filaments, whose resistance changes with voltage.
- Using the supply voltage instead of the voltage across that resistor.
- Unit prefix slips: with R in kΩ and I in mA the product is in volts directly.
Statistics and uncertainty
The formula is deterministic for an ideal resistor. Real resistors have a tolerance (for example ±1% or ±5%) and meters have measurement error, so R and I are known only within a band. For independent errors, δV/V ≈ √[(δI/I)² + (δR/R)²].
Where it is used
- Finding the current a given voltage drives through a load.
- Voltage drop along a cable of known resistance.
- Choosing a series resistor for an LED or a sensor.
Maths you need
- Proportionality: V is proportional to I when R is constant
- Rearranging equations: solving V = IR for I or R