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Resistivity of Materials: Formula, Unit, and Examples

Resistance is the physical property of the material which opposes the current flow in the circuit whereas resistivity is the intrinsic property that helps us understand the relation between the dimension of the substance and the resistance offered by it. 

In this article, we will learn about Resistance, Resistivity, how resistance and resistivity are related to each other, the difference between resistance and resistivity, and others in detail.

Resistance Definition

Let’s consider water flowing through a pipe encounters resistance to its flow like bending or squeezing of pipe, then the flow of water is decreased significantly. Similarly, if the current is considered as water and the pipe is considered to be the conductor through which the current is flowing, then bending and squeezing or any other form of disturbance can be visualized as resistance.

Resistance is the property of substance due to which is opposes the current flowing through the conductor, and according to ohm’s law for resistance, 

R = V/I

Where,

  • R is Resistance of the conductor
  • V is Voltage across the conductor
  • I is Current across the conductor.

Unit of Resistance

SI unit of the resistance is “ohms” which is denoted by Ω

Resistivity Definition

When a voltage is applied to a conductor, the electric field E is created inside it which pushes the charges to move. The current density that gets developed depends on the material and the electric field that is created. This density can be very complex but under reasonable assumptions, including assuming the metals are at room temperature. This relation can be modeled using, 

J = σE

Here, σ is the electrical conductivity.

Electrical conductivity is the measure of the material to conduct electricity. Conductors have more electrical conductivity than insulators. Conductivity is an intrinsic property of material, another intrinsic property of the material is the resistivity of electrical resistivity. It is a measure of how strongly a material opposes the flow of charges. It is denoted by the lowercase Greek letter rho(ρ). The electrical resistivity is reciprocal of the electrical conductivity.   

ρ = 1/σ

Electrical Resistivity measures the intrinsic resistance of the material and is the fundamental property of the material. Other than depending on the electrical conductivity, resistivity also depends upon the temperature, type of material, impurities in the material, and the physical structure of the material as well. Generally, metals have low resistivity, which means they are good conductors and non-metals have high resistivity, which means they are bas conductors.

Resistivity Formula

The formula to calculate the resistivity of any material is,

ρ = RA/l

where,

  • ρ is the resistivity of the material and is measured in Ω.m
  • R is the electrical resistance of uniform cross-sectional material and is measured in Ω
  • l is the length of a piece of material and is measured in m
  • A is the cross-sectional area of the material and is measured in m2

We can also measure the resistivity of the material if the Electric Field and Current Density are given as,

ρ = E/J

where,

  • ρ is the resistivity of the material and is measured in Ω.m
  • E is the magnitude of the electric field and is measured in V.m-1
  • J is the magnitude of current density and is measured in A.m-2

Learn more about, Resistance Formula

Unit of Resistivity

  • The SI unit of resistivity is ohm-meter which is denoted by Ω-m.
  • In the CGS system, the unit of Resistivity is Ω-cm.
  • The dimension of resistivity is M1L3T-3A-2

Resistivity of Different Materials

The table for resistivity and conductivity for various materials is given as follows:

Material

Resistivity, ρ (Ω⋅m)

Conductivity, σ (Ω⋅m)−1

Conductors

Silver

1.59×10−8

6.29×107

Copper

1.68×10−8

5.95×107

Gold

2.44×10−8

4.10×107

Aluminum

2.65×10−8

3.77×107

Iron

9.71×10−8

1.03×107

Lead

22.00×10−8

0.45×107

Mercury

98.00×10−8

0.10×107

Nichrome (Ni, Fe, Cr alloy)

100.00×10−8

0.10×107

Platinum

10.60×10−8

0.94×107

Tungsten

5.60×10−8

1.79×107

Semiconductors

Carbon (Pure)

3.50×10−5

2.86×104

Carbon

(3.5−60)×10−5

(2.86−1.67)×10-6

Silicon (Pure)

2300

–

Silicon

0.1 – 2300

–

Insulators

Glass

109−1014

10−9−19−14

Mica

1011−1015

10−11−10−15

Quartz (Fused)

75×1016

1.33×10−18

Rubber (Hard)

1013−1016

10−13−10−16

Wood

108−1011

10−8−10−11

Relation of Resistance and Resistivity

As our previous analogy of resistance, where resistance is analogous to the water. The resistance in the flow of water is directly proportional to the length (the longer the pipe harder to pump water through it)of the pipe and inversely proportional to the cross-sectional area of the pipe (the wider the pipe, the more water can flow through it), similarly, resistance offered by a conductor is directly proportional to the length of conductor and inversely proportional to the cross-sectional area of the conductor.

Relation Between Resistance and Resistivity

 

Thus, the resistance of the conductor is given by, 

R ∝ l/A

R = ρl/A

where, R is Resistance

l is length of wire

A is cross sectional area of wire

ρ is Resistivity

Specific Resistivity

The resistivity of material for the unit length and unit cross-sectional area is called Specific Resistivity and it means how strongly a material with unit length and unit cross-sectional area, can resist the flow of current. 

In other words, specific resistivity the resistance of the material, if it’s the length and cross-sectional area, becomes unity.

R = (ρ×1)/1

R =  ρ

Difference Between Resistance and Resistivity

There are various differences between Resistance and Resistivity, some of those differences are as follows:

Resistance

Resistivity

Resistance of the substance is its physical property of resisting the flow of current i.e. electrons.Resistivity of the substance is its intrinsic property and is the measure of how strongly the substance can resist the flow of current.

Resistance is directly proportional to the length and temperature while it is inversely proportional to the cross-sectional area of the material i.e., 

ρ = (R×A)/l

Where R is resistance, l is the length of the conductor, and A is the cross-sectional area of the conductor.

Resistivity only depends on the temperature, type of material, impurities, physical structure, and conductivity of the material. As

ρ = 1/σ

Where σ is the conductivity of the material.

In electrical circuits, resistance is represented by R.In electrical circuits, resistivity is denoted by ρ

The formula for calculating the resistance of a circuit is given by Ohm’s law i.e., R = V/I 

Where V is voltage and  I is current passing through the material.

The formula for calculating the resistivity is given by  J = σE or \rho = \frac{1}{\sigma}

Where J is the current density, E is the electric field intensity, and σ is the conductivity of the material.

SI unit of resistance is the ohm(Ω).SI unit of Resistivity is ohm-meter (Ω-m).

Resistor Colour Coding

Resistors are used to control the flow of the current in the electric circuit. The resistance in the resistor is shown using different color codes. Different color codes in the resistor specify different values of the resistance.

A resistor has four different color codes that specify the value of resistance of the resistor. The color in the resistor band specifies different values of the resistance, such as black color specifies the 0 value, and brown color specifies the 10 value with ±1% tolerance.

Read More,

Sample Problems on Resistance and Resistivity

Problem 1: A battery of 5 Volts connected to a conductor induces a current of 10mA in the conductor. Find the resistance of the conductor. 

Answer: 

Resistance of conductor is given by the relation, 

R  = V/I 

Given: 

  • V = 5 V 
  • I = 10 mA = 0.01 A 

Plugging in the values inside the relation, 

R = V/I 

⇒ R = (5)/(0.01) 

⇒ R= 500 Ω

Problem 2: A battery of 20 Volts connected to a conductor induces a current of 50mA in the conductor. Find the resistance of the conductor. 

Answer: 

Resistance of conductor is given by the relation, 

R  = V/I 

Given: 

  • V = 20 V 
  • I = 50 mA = 0.05 A 

Plugging in the values inside the relation, 

R = V/I 

⇒ R = (20)/(0.05) 

⇒ R= 400 Ω

Problem 3: A battery of 100 Volts connected to a material induces a current of 0 mA in the conductor. Find the resistance of the material. 

Answer: 

Resistance of conductor is given by the relation, 

R  = V/I 

Given: 

  • V = 20 V
  • I = 0 mA = 0 A 

Plugging in the values inside the relation, 

⇒ R = (20)/(0) = Not defined

Resistance approaches to infinity, which means the material is an insulator. 

Problem 4: A cylindrical conductor of length 0.5m and cross-sectional area 0.01 m2. The resistivity of the material is 2 x 10-8 ohm-m. Find the resistance of the material. 

Answer: 

Resistance of a conductor is given by, 

 ρ = (R×A)/l

Given: 

  • l = 0.5m
  • A = 0.01 m2
  • ρ = 2 x 10-8 

Plugging the values in the relation given above,

⇒ R = \frac{2 \times 10^{-8} 0.5}{0.01}

⇒ R = 10-6 Ω

Problem 5: A cylindrical conductor of length 2m and cross-sectional area 0.05 m2. The resistivity of the material is 4 x 10-8 ohm-m. Find the resistance of the material. 

Answer: 

Resistance of a conductor is given by, 

  ρ = (R×A)/l

Given: 

  • l = 2m
  • A = 0.05 m2
  • ρ = 4 × 10-8 

Plugging the values in the relation given above,

⇒ R = \frac{4 \times 10^{-8} 2}{0.05}

⇒ R = 1.6 × 10-6 Ω

FAQs on Resistance and Resistivity

Q1: What is Resistance?

Answer:

Resistance is the physical property of the material to resist the flow of electricity passing through it when an external voltage is applied.

Q2: What is Resistivity?

Answer:

Electrical resistivity of the intrinsic property of the material and is a measure of how strongly the material can resist the flow of current through it.

Q3: How are Resistance and Resistivity related?

Answer:

Resistance and resistivity are related by the formula which is given by:

R = ρl/A

Where,

  • R is the resistance of the conductor, 
  • l is the length of the conductor, 
  • A is the cross-sectional area of the conductor, and 
  • ρ is the proportionality constant which represents resistivity.

Q4: What is the Difference between Resistance and Resistivity?

Answer:

The key difference between resistance and resistivity is that resistance is the physical property of the material i.e., it depends on the physical things like dimensions of the material. On the other side resistivity is the intrinsic property i.e., it is the inherent property of the substance and doesn’t depend on physical factors.

Q5: What is SI unit of Electrical Resistivity?

Answer:

The SI unit of Electrical Resistivity is Ω-m.


 


Reffered: https://www.geeksforgeeks.org

Class 10

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