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Resistance is the opposition to the flow of current in a circuit. Understanding resistance and Ohm's law is fundamental to analysing any electrical circuit. This lesson covers the definition of resistance, the conditions under which Ohm's law applies, and the factors that affect the resistance of a conductor.
Resistance is defined as the ratio of the potential difference across a component to the current flowing through it:
R=IV
where:
One ohm is the resistance of a component when a potential difference of one volt drives a current of one ampere through it (1 Ω = 1 V A⁻¹).
Key Point: The equation R = V/I is the definition of resistance. It applies to ALL components, whether or not they obey Ohm's law. Do not confuse this definition with Ohm's law itself.
Ohm's law states that the current through a conductor is directly proportional to the potential difference across it, provided the physical conditions (especially temperature) remain constant.
Mathematically: V ∝ I (at constant temperature)
This means V/I = constant, i.e., the resistance is constant.
A component that obeys Ohm's law is called an ohmic conductor. Its I-V graph is a straight line through the origin.
Ohm's law only holds when:
Most metallic conductors obey Ohm's law at constant temperature. Components like filament lamps, thermistors, and diodes do NOT obey Ohm's law because their resistance changes with current (due to temperature changes or their non-linear nature).
Common Misconception: Many students think V = IR is Ohm's law. It is not — V = IR is simply the definition of resistance rearranged. Ohm's law is the specific statement that V and I are proportional (constant R) under constant physical conditions.
The resistance of a uniform conductor depends on:
| Factor | Effect on resistance | Relationship |
|---|---|---|
| Length (L) | Longer wire → greater resistance | R ∝ L |
| Cross-sectional area (A) | Thicker wire → less resistance | R ∝ 1/A |
| Material (resistivity, ρ) | Different materials have different resistivities | R ∝ ρ |
| Temperature | Usually increases R for metals | Complex relationship |
These combine into the resistivity equation:
R=AρL
(This is covered in detail in Lesson 5 on Resistivity.)
A longer wire means charge carriers must travel further and undergo more collisions with the lattice ions. Each section of wire adds more resistance, so resistance is proportional to length.
A wider wire provides more "lanes" for charge carriers to flow through. Doubling the cross-sectional area is like having two identical resistors in parallel — each carries half the current, effectively halving the total resistance.
In metals, when temperature increases:
For metals, resistance increases approximately linearly with temperature over moderate ranges.
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