Define resistance and its unit. What is the cause of resistance? On what factors does the resistance of a metallic conductor depend?

Definition of Resistance

Resistance ($R$) is the opposition offered by a material to the flow of electric current. It determines how much a conductor resists the movement of free electrons when a voltage is applied.

Mathematically, resistance is given by Ohm’s Law:

R=V/I​

where:

• R = Resistance (Ohms, Ω)
• $V$ = Voltage (Volts, V)
• $I$ = Current (Amperes, A)

Unit of Resistance

The SI unit of resistance is the Ohm (Ω), where:

1Ω=1V/1A​

This means a conductor has a resistance of 1 ohm if a current of 1 ampere flows through it when a voltage of 1 volt is applied.

Cause of Resistance

Resistance occurs due to collisions between free electrons and atoms (or ions) in a conductor. As electrons move through a material under an electric field, they scatter due to these collisions, impeding their flow and causing energy loss in the form of heat.

Factors Affecting the Resistance of a Metallic Conductor

The resistance ($R$) of a conductor depends on the following factors:

1. Length of the Conductor ($L$)

   • Resistance is directly proportional to length: R∝L
   • A longer wire has more atomic collisions, increasing resistance.

2. Cross-Sectional Area ($A$)

   • Resistance is inversely proportional to area: R∝1/A​
   • A thicker wire allows more electrons to pass, reducing resistance.

3. Material of the Conductor

   • Different materials have different resistivities (ρ), a measure of intrinsic resistance.
   • Good conductors (copper, silver) have low resistivity, while poor conductors (nichrome, tungsten) have high resistivity.

4. Temperature

   • For metallic conductors, resistance increases with temperature because atoms vibrate more, causing more collisions.
   • For semiconductors, resistance decreases with temperature as more free electrons become available.

5. Nature of the Conductor (Impurities & Structure)

   • Impurities increase resistance as they disrupt electron movement.
   • Crystal structure and defects can also affect resistance.

Formula for Resistance

Using the above factors, resistance is given by the formula:

R=ρL/A​

where:

• R = Resistance (Ω)
• ρ = Resistivity (Ω⋅m) (depends on the material)
• $L$ = Length of the conductor (m)
• A = Cross-sectional area (m²)

Conclusion

Resistance is a crucial property of materials that affects electrical circuits. It depends on length, area, material, temperature, and impurities. Understanding these factors helps in designing electrical components for efficient energy transfer.