For a linear resistor, current is proportional to the potential difference across it. The constant of proportionality is the resistance. This relationship is Ohm’s law and it holds for many conductors over a useful operating range, but not for every device: a diode, a lamp filament or a motor does not follow a straight-line voltage-current characteristic.
Ohm’s law in three forms
Current through a resistor
Problem. A 12 V supply is connected across a 4 Ω resistor. Find the current.
Solution. I = V ÷ R = 12 V ÷ 4 Ω = 3 A.
Resistance, heat and tolerance
Resistance converts electrical energy into heat. A resistor with a power rating below the actual dissipation overheats and drifts or fails. The rated value of a practical resistor also carries a tolerance, so the real resistance lies within a band around the nominal value.
Resistance from a measurement
Problem. A current of 20 mA flows when 9 V is applied across a resistor. What is its resistance?
Solution. R = V ÷ I = 9 V ÷ 0.020 A = 450 Ω.
- Voltage is measured across a component, in parallel.
- Current is measured through a component, in series.
- Resistance is measured with the component isolated from the supply.
- Tolerance and temperature change the real value, so measure when the result matters.
- Ohm’s law is V = I × R for a linear resistance.
- The same relation rearranges to I = V/R and R = V/I.
- Real resistors have tolerance and a power rating.
- Non-ohmic devices need their own characteristic curve.
Worked example
A 9 V source drives 30 mA through a resistor: R = 9 ÷ 0.030 = 300 Ω. The resistor dissipates P = V × I = 9 × 0.030 = 0.27 W, so a 0.25 W part would be marginal and a higher-rated part is the safer choice.