The resistance of a metallic conductor is determined by four main factors.
Here is a list and explanation of each factor:
1. Length of the Conductor (L)
- Relationship: Resistance is directly proportional to the length of the conductor.
- Explanation: The longer the conductor, the farther the electrons have to travel. This increases the number of collisions they have with the metal ions, which impedes their flow.
- Analogy: Think of it like a hallway. A longer hallway takes more time and effort to walk through than a shorter one.
Rule: Double the length, and you double the resistance (all other factors being equal).
2. Cross-Sectional Area (A)
- Relationship: Resistance is inversely proportional to the cross-sectional area of the conductor.
- Explanation: A wider conductor (larger cross-sectional area) provides more pathways for the electrons to flow, reducing congestion and the overall opposition to the current.
- Analogy: A wide, multi-lane highway can handle more traffic with less congestion than a narrow, single-lane road.
Rule: Double the cross-sectional area, and you halve the resistance.
3. Material of the Conductor (Resistivity, ρ)
- Relationship: Resistance is directly proportional to the resistivity of the material.
- Explanation: Resistivity (ρ) is an intrinsic property of a material that measures how strongly it resists the flow of electric current. Different materials have different atomic structures and numbers of free electrons, making them inherently better or worse at conducting electricity.
- Good Conductors: Materials like silver, copper, and gold have low resistivity.
- Poor Conductors (Resistors): Materials like nichrome and tungsten have high resistivity.
- Analogy: Walking on a smooth, paved sidewalk (low resistivity) is much easier than wading through thick mud (high resistivity).
4. Temperature (T)
- Relationship: For metallic conductors, resistance is directly proportional to the temperature.
- Explanation: As the temperature of a metal increases, its atoms (ions in the crystal lattice) vibrate more vigorously. These increased vibrations cause more frequent collisions with the flowing electrons, making it more difficult for the current to pass through.
- Note: This relationship is true for most metals (which have a positive temperature coefficient). However, for semiconductors and insulators, resistance typically decreases as temperature increases.
Rule: Heat a metal wire, and its resistance will increase.
Summary Formula
These factors are neatly summarized in the formula for resistance:
$R = \frac{ρL}{A}$
Where:
R is the Resistance (in Ohms, Ω)
ρ (rho) is the Resistivity of the material (in Ohm-meters, Ω·m)
L is the Length of the conductor (in meters, m)
A is the Cross-sectional Area of the conductor (in square meters, m²)
(Note: Temperature is not explicitly in this formula, as resistivity (ρ) itself is temperature-dependent.)
