Resistance and Resistivity
What is Resistance?
Definition
Resistance
Resistance is a measure of how much a material opposes the flow of electric current.
It determines how easily electrons can move through a conductor.Note
The unit of resistance is the ohm (Ω).
The Formula for Resistance
Resistance is defined by the equation:
$$R = \frac{V}{I}$$
where:
- $R$ is the resistance in ohms (Ω)
- $V$ is the potential difference across the conductor in volts (V)
- $I$ is the current flowing through the conductor in amperes (A)
If a potential difference of 12 V is applied across a resistor and a current of 2 A flows through it, the resistance is:
$$R = \frac{12 \, \text{V}}{2 \, \text{A}} = 6 \, \Omega$$
Ohm’s Law and Resistance
Definition
Ohm's law
Ohm’s Law states that the current through a conductor is directly proportional to the potential difference across it, provided the temperature remains constant.
For ohmic materials (those that obey Ohm’s Law), the resistance remains constant regardless of the current or voltage.Example
A graph of current (I) versus voltage (V) for an ohmic material is a straight line through the origin, indicating constant resistance.
- Not all materials obey Ohm’s Law.
- For non-ohmic materials, such as filament lamps or diodes, the resistance changes with current or voltage.
- Resistance in a wire originates from the collisions between free electrons and the metal atoms in the conductor.
- As electrons move through the wire, they interact with the vibrating lattice of atoms, losing energy in the form of heat.
- The higher the temperature or the longer and thinner the wire, the greater the resistance.
Factors Affecting Resistance
Resistance depends on several factors:
- Material:
- Different materials have different abilities to conduct electricity.
- Metals like copper have low resistance, while insulators like rubber have high resistance.
- Length:
- Resistance is directly proportional to the length of the conductor.
- A longer wire has more resistance.
- Cross-Sectional Area:
- Resistance is inversely proportional to the cross-sectional area.
- A thicker wire has less resistance.
- Temperature:
