The Role of Resistivity or Specific Resistance in Electrical Engineering

Resistivity or Specific Resistance:

Resistivity (also called specific resistance) is a fundamental property of a material that quantifies how strongly it resists the flow of electric current. It is denoted by the symbol ρ (rho) and is typically measured in ohm-meters (Ω·m) in the International System of Units (SI). The higher the resistivity, the more the material resists the flow of current.

The resistivity depends on the nature of the material, temperature, and other factors. For instance, metals like copper and aluminum have low resistivity, meaning they allow current to pass through easily, while materials like rubber or wood have high resistivity, making them poor conductors of electricity.

The formula for resistivity can be expressed as:  R = ρL /A

Where:

• R is the resistance in ohms (Ω)
• ρ is the resistivity in ohm-meters (Ω·m)
• L is the length of the material (in meters)
• A is the cross-sectional area (in square meters)

This relationship shows that resistance is directly proportional to the resistivity and length of the material and inversely proportional to the cross-sectional area.

List of Common Conductors Of Specific Resistance:

Here’s a list of common conductors with their approximate resistivity (specific resistance) values at room temperature (20°C):

1. Silver (Ag)
   • Resistivity: 1.59×10−8 Ω-m
2. Copper (Cu)
   • Resistivity: 1.68×10−8 Ω-m
3. Gold (Au)
   • Resistivity: 2.44×10−8 Ω-m
4. Aluminum (Al)
   • Resistivity: 2.82×10−8 Ω-m
5. Iron (Fe)
   • Resistivity: 9.71×10−8 Ω-m
6. Nickel (Ni)
   • Resistivity: 6.99×10−8 Ω-m
7. Platinum (Pt)
   • Resistivity: 10.6×10−8 Ω-m
8. Tungsten (W)
   • Resistivity: 5.60×10−7 Ω-m
9. Lead (Pb)
   • Resistivity: 2.20×10−7 Ω-m
10. Mercury (Hg)
    • Resistivity: 9.58×10−7 Ω-m

Insulating Materials (for comparison):

• Rubber: 10¹³ Ω-m (very high resistivity)
• Wood: 10¹² Ω-m (high resistivity)

Note: The resistivity values for conductors like copper, silver, and gold are very low, making them excellent for electrical wiring and circuits, whereas materials like rubber and wood are high resistivity and are used as insulators.

Temperature Coefficient of Resistance:

The temperature coefficient of resistance (often denoted as α) refers to how the resistance of a material changes with temperature. It quantifies the rate at which the resistance increases or decreases as the temperature changes. For most conductors, resistance increases with an increase in temperature, while for some semiconductors and insulators, the resistance decreases as temperature increases.

Formula:

The temperature coefficient of resistance is typically expressed as:

R_T=R₀(1+α(T−T₀))

Where:

• R_T​ is the resistance at temperature T,
• R₀ is the resistance at the reference temperature T₀ (usually taken as 20°C),
• α is the temperature coefficient of resistance (in )
• T is the temperature at which the resistance is being measured.

For conductors, the temperature coefficient (α) is typically positive, meaning their resistance increases as temperature rises. On the other hand, for semiconductors and insulators, α is negative because their resistance decreases with increasing temperature.

Typical Values of Temperature Coefficient of Resistance for Common Materials:

1. Silver (Ag):
   • α≈0.0038 per∘C
2. Copper (Cu):
   • α≈0.0039 per∘C
3. Gold (Au):
   • α≈0.0034 per∘C
4. Aluminum (Al):
   • α≈0.0040 per∘C
5. Iron (Fe):
   • α≈0.0050 per∘C
6. Platinum (Pt):
   • α≈0.0039 per∘C
7. Nickel (Ni):
   • α≈0.0065 per∘C

Semiconductors:

• Silicon (Si):
  • α≈−0.0001 per∘C (Negative coefficient, resistance decreases as temperature increases)
• Germanium (Ge):
  • α≈−0.0002 per∘C (Negative coefficient, resistance decreases as temperature increases)

Insulators:

• Materials like rubber or wood typically have a very low and negative temperature coefficient, meaning their resistance can decrease with increased temperature under certain conditions.

Practical Implications:

• For conductors, knowing the temperature coefficient is important for designing electrical circuits, especially in systems exposed to temperature variations. High temperature can cause a significant increase in resistance, affecting performance.
• For semiconductors, the negative temperature coefficient is important for devices like thermistors, which change resistance in response to temperature, and in applications like temperature sensors or in thermoelectric effects.

Drift Velocity:

Drift velocity refers to the average velocity of charged particles (usually electrons) in a conducting material under the influence of an electric field. When an electric field is applied to a conductor, the free electrons inside the conductor accelerate towards the positive end of the material, but due to frequent collisions with atoms in the material, they don’t accelerate indefinitely. Instead, they move with a constant average velocity, known as the drift velocity.

Formula for Drift Velocity:

The drift velocity v_d​ can be expressed as:                v_d​ = I / nAe

Where:

• v_d​ is the drift velocity (in meters per second, m/s),
• I is the electric current flowing through the conductor (in amperes, A),
• n is the number of charge carriers per unit volume (in m^-3 )
• A is the cross-sectional area of the conductor (in square meters m²),
• e is the charge of an electron (1.6×10-¹⁹ C

Mobility: Mobility is the average drift velocity per unit field.