resistivity

Physics Notes: Resistivity, Resistance, Conductivity & Ohm's Law

1. Resistivity (ρ)

Definition

Resistivity is a property of a material that measures how strongly it opposes the flow of electric current.

  • Symbol: ρ (rho)

  • High resistivity → Difficult for electrons to move

  • Low resistivity → Easy for electrons to move

Examples

Low Resistivity (Good Conductors)

  • Copper

  • Silver

  • Gold

  • Aluminum

High Resistivity (Insulators)

  • Rubber

  • Plastic

  • Glass

  • Wood (dry)

2. Conductivity

Definition

Conductivity measures how easily electricity flows through a material.

Conductivity is the opposite of resistivity.

High conductivity

↓

Low resistivity

↓

Easy electron flow

3. Resistance (R)

Definition

Resistance measures how difficult it is for electric current to flow through a conductor.

  • Symbol: R

  • Unit: Ohm (Ω)

Higher resistance means:

  • Less current

  • Harder electron movement

Lower resistance means:

  • More current

  • Easier electron movement

4. Factors Affecting Resistance

Resistance depends on four factors.

A. Resistivity (ρ)

Higher resistivity

↓

Higher resistance

Relationship:

[
\boxed{R\propto\rho}
]

B. Length (L)

Longer wire

↓

Higher resistance

Reason:

Electrons travel farther and collide more often.

Relationship:

[
\boxed{R\propto L}
]

C. Cross-Sectional Area (A)

Thicker wire

↓

Lower resistance

Reason:

More space for electrons to flow.

Relationship:

[
\boxed{R\propto\frac1A}
]

D. Temperature

Higher temperature

↓

Atoms vibrate more

↓

More electron collisions

↓

Higher resistance

For most conductors:

Higher temperature

↓

Higher resistivity

↓

Higher resistance

5. Superconductors

Definition

Superconductors are materials with zero electrical resistance at extremely low temperatures.

Properties

  • No energy loss

  • Perfect conductivity

  • No electrical friction

Applications

  • MRI machines

  • Particle accelerators

  • Magnetic levitation (Maglev) trains

6. Resistance Formula

Resistance depends on:

  • Resistivity

  • Length

  • Cross-sectional area

Formula

[
\boxed{R=\frac{\rho L}{A}}
]

Where

  • R = Resistance (Ω)

  • ρ = Resistivity

  • L = Length (m)

  • A = Cross-sectional area (m²)

7. Formula Relationships

Increase resistivity

↓

Resistance increases

Increase length

↓

Resistance increases

Increase cross-sectional area

↓

Resistance decreases

Summary

[
\boxed{R\propto\frac{\rho L}{A}}
]

8. Quick Effects Table

Change

Resistance

Increase resistivity

Increases

Decrease resistivity

Decreases

Increase length

Increases

Decrease length

Decreases

Increase area

Decreases

Decrease area

Increases

Increase temperature

Usually increases

9. Georg Ohm

Georg Ohm discovered the relationship between:

  • Voltage

  • Current

  • Resistance

His work became known as Ohm's Law.

10. Ohm's Law

Formula

[
\boxed{V=IR}
]

Where

  • V = Voltage (Volts)

  • I = Current (Amps)

  • R = Resistance (Ohms)

11. Rearranged Ohm's Law

To find current:

[
\boxed{I=\frac{V}{R}}
]

To find resistance:

[
\boxed{R=\frac{V}{I}}
]

12. Triangle Trick

      V
     ----
     I  R

Cover the unknown.

Examples:

Find voltage

V = I × R

Find current

I = V ÷ R

Find resistance

R = V ÷ I

13. Circuit Variables

Quantity

Symbol

Unit

Meaning

Water Analogy

Voltage

V

Volt (V)

Energy per charge

Water pressure

Current

I

Ampere (A)

Flow of charge

Water flow

Resistance

R

Ohm (Ω)

Opposition to flow

Narrow pipe

14. Relationships in Ohm's Law

Increase voltage

↓

Current increases

(Resistance constant)

Increase resistance

↓

Current decreases

(Voltage constant)

Higher voltage

↓

More current

Higher resistance

↓

Less current

15. Example 1

Find Voltage

Given

Current:

[
I=10.0A
]

Resistance:

[
R=11.0\Omega
]

Formula

[
V=IR
]

Calculation

[
V=(10.0)(11.0)
]

[
\boxed{V=110V}
]

Answer:

110 volts

16. Example 2

Find Current

Given

Voltage:

[
V=110V
]

Resistance:

[
R=2800\Omega
]

Formula

[
I=\frac VR
]

Calculation

[
I=\frac{110}{2800}
]

[
I=0.039A
]

Answer:

[
\boxed{0.039A}
]

17. Example 3

Find Resistance

Given

Voltage:

[
V=9.0V
]

Current:

[
I=0.50A
]

Formula

[
R=\frac VI
]

Calculation

[
R=\frac9.0{0.50}
]

[
\boxed{R=18\Omega}
]

Answer:

18 ohms

18. Resistance Examples

Which wire has the least resistance?

✔ Thick

✔ Short

✔ Cold

✔ Copper

Which wire has the most resistance?

✔ Thin

✔ Long

✔ Hot

✔ Rubber

19. Important Unit Symbols

Quantity

Symbol

Unit

Voltage

V

Volt (V)

Current

I

Ampere (A)

Resistance

R

Ohm (Ω)

Resistivity

ρ

Ω·m

Area

A

m²

Length

L

m

20. Essential Formulas

Resistance

[
\boxed{R=\frac{\rho L}{A}}
]

Ohm's Law

[
\boxed{V=IR}
]

Current

[
\boxed{I=\frac VR}
]

Resistance

[
\boxed{R=\frac VI}
]

Voltage

[
\boxed{V=IR}
]

Summary

  • Resistivity (ρ) is a material property that describes how strongly a material opposes electric current.

  • Conductivity is the opposite of resistivity; good conductors have low resistivity.

  • Resistance (R) depends on resistivity, wire length, cross-sectional area, and temperature.

  • Longer, thinner, hotter wires have greater resistance; shorter, thicker, colder wires have lower resistance.

  • Superconductors have essentially zero resistance at extremely low temperatures.

  • Ohm's Law relates voltage, current, and resistance:

[
\boxed{V=IR}
]

with the equivalent forms:

[
\boxed{I=\frac{V}{R}}
]

[
\boxed{R=\frac{V}{I}}
]

These equations are the primary formulas used to solve basic circuit problems.