Resistance and Ohm's law
Resistance is the opposition of a conductor to the flow of current. It is measured in ohms (Ω). Ohm's law states that the current through a metallic conductor is directly proportional to the potential difference across it, provided the temperature stays constant.
This gives the equation V = I R, or R = V / I. A component that obeys Ohm's law is called an ohmic conductor and its V–I graph is a straight line through the origin. A filament lamp is non-ohmic: its resistance rises as it gets hotter, so its graph curves.
Key formula
V = I R and R = V / I
V in volts, I in amperes, R in ohms (Ω).
Factors affecting resistance
For a wire of a given material, resistance depends on four factors:
- Length (L): R is directly proportional to length — a longer wire has more resistance.
- Cross-sectional area (A): R is inversely proportional to area — a thicker wire has less resistance.
- Type of material: described by the resistivity ρ.
- Temperature: for metals, resistance increases with temperature.
These combine as R = ρL / A, where ρ is the resistivity in Ω m.
Worked example
A p.d. of 12 V is applied across a resistor and a current of 0.5 A flows. Find its resistance. If the same resistor is replaced by a wire twice as long of the same material and area, what is the new resistance?
R = V / I = 12 / 0.5 = 24 Ω.
Since R ∝ L, doubling the length gives 48 Ω.
Remember
- Ohmic conductor: straight-line V–I graph through the origin.
- Longer or thinner wire → higher resistance.
- Resistors in series add: R = R₁ + R₂; in parallel 1/R = 1/R₁ + 1/R₂.