What does Ohm's law say?
Voltage (potential difference, V) pushes electric charge around a circuit. The flow of charge is the current (I). Every material resists this flow a little; that opposition is its resistance (R), measured in ohms (Ω).
Ohm's law says that if the temperature stays the same, doubling the voltage doubles the current. The ratio V/I stays constant, and that constant is the resistance.
The V–I graph
If you plot voltage against current for a metal wire, you get a straight line through the origin. The slope of the V–I line equals the resistance. A steeper line means higher resistance. Devices that give a straight line are called ohmic; bulbs (which heat up) and diodes are non-ohmic.
What does resistance depend on?
For a wire, R = ρL/A. Resistance increases with length (L), decreases with cross-section area (A), and depends on the material through its resistivity (ρ). For most metals it also increases with temperature.
Try it in the circuit
Use the sliders in the animation to change the battery voltage and the resistor. Watch the moving charges speed up or slow down, and read the ammeter.
Key formulas and definitions
- V = I × R
- I = V / R, R = V / I
- Units: V in volts (V), I in amperes (A), R in ohms (Ω)
- R = ρL / A (resistance of a wire)
Worked examples
1. A 12 V battery is connected to a 4 Ω resistor. Find the current.
I = V / R = 12 / 4 = 3 A.
2. A current of 0.5 A flows through a lamp when 230 V is applied. Find its resistance.
R = V / I = 230 / 0.5 = 460 Ω.
3. What voltage is needed to push 2 A through a 15 Ω heater?
V = I × R = 2 × 15 = 30 V.
Common mistakes
- Using milliamps without converting: 200 mA = 0.2 A.
- Thinking Ohm's law works for every device. Bulbs and diodes do not give a straight V–I line.
- Saying resistance depends on voltage. For an ohmic conductor R stays constant; V and I change together.
- Mixing up the V–I and I–V graph slopes: V–I slope = R, I–V slope = 1/R.