[Physics Class Notes] on Difference Between Resistance and Resistivity Pdf for Exam

We define the resistance of a conductor as the obstruction posed by the conductor to the flow of electric current through it.

 

Ohm’s law states that the current (I)  flowing through the conductor is directly proportional to the potential difference (V) across the ends of the conductor, provided conditions like temperature, the mechanical strain of the conductor remains constant. The formula is given by,                         

Where R is called resistance of the conductor and is defined as the ratio of potential difference (V) across the ends of the conductor to the current (I) flowing through it.

 

The laws of resistance are as the following:

1. R is directly proportional to conductor length when temperature and other physical aspects are maintained as same.

2. R is inversely proportional to the cross-sectional area of the conductor when the other factors are the same condition.

 

Define Resistance and Resistivity

Resistance 

Resistance is a force, such as friction, that operates opposite to the direction of motion of a body (motion of current) and tends to decelerate or slow down the body’s motion. A  measure of the degree to which a conductor impedes the flow of electric current induced by a voltage. Resistance is measured in ohms.

 

For example, when you’re driving a car as you accelerate it (apply potential difference), the speed of the car increases (high current starts flowing). As you encounter a speed-breaker (resistance), you decelerate it and the speed of the car reduces (the flow of current is obstructed). This is how you control the speed of your car (damage to the circuit by high current flow).

 

Factors Affecting Resistance

1. The resistance of the material depends on the following factors.

2. It is inversely proportional to the cross-section area of the conductor.

3. The resistance of the material depends on its temperature.

4. With the increase in the length of the conductor, the resistance of the material increases.

5. It is directly proportional to the material. 

 

Temperature Coefficient of Resistance

A slight change in resistance of a substance per kelvin is called the temperature coefficient of resistance. 

 

Thus, mathematically it is expressed as follows:

 

a = Rt – R0 / R0t

 

Where

 

R0 is the Resistance of material at 0 °C.

 

Rt is the Resistance of material at t temperature.

 

t is the change in temperature.

 

α is the Temperature coefficient of resistance.

 

Resistivity

Resistivity of a material is defined as the resistance offered by unit length and unit cross-sectional area by a wire of the material of the conductor.

 

Resistance of a conductor depends upon various factors such as

 

Factors affecting Resistivity

The following factors affect the resistivity, 

• The temperature of the material

• The nature of the material 

• Resistivity is independent of the dimensions of a conductor.

 

Temperature Coefficient of Resistivity

A slight change in resistivity of a material per kelvin is called the temperature coefficient of resistivity.

 

Thus, mathematically it can be expressed as follows:

 

a = ρt – ρ0 / ρ0t

 

Where

 

ρ0 is the resistivity of material at 0 °C.

 

ρt is the resistivity of material at temperature t °C.

 

t is the change in temperature

 

α is the temperature coefficient of Resistivity.

 

The SI unit of the temperature coefficient of resistance/resistivity (α) is per kelvin (1/K or K-1)

 

Length and Cross-sectional Area

Suppose you are constructing a speed-breaker in your area to prevent accident cases. The road is 20 m in length and builds the same from one end of the road to another. In this manner, accidents won’t happen in your vicinity because the resistance is high.

 

We can conclude here that:    

                  

 

In another case, you divide the road into two halves and make that one-way road as a two-way road by constructing a median in between. This is how you used a smart approach to prevent accidents.

 

Here, you reached the conclusion that by dividing the area into two halves; the resistance gets doubled. It means the accidents didn’t happen because the current got divided instead of a large flow of current (vehicles) flowing in a single path.

 

So    

            

 

Here, A is the cross-sectional area of the conductor.

 

Now combining eq(1) and (2), we get ,

 

 

Here, L is the length of the conductor.

 

Resistance Formula with Resistivity

Now, removing the proportionality sign, we get a proportionality constant given by,

                    

 

Here,  ρ is called the specific resistivity or electrical resistivity of the material of the conductor.

 

The unit of A is (meter square) m² and that of L is meter(m).

 

SI unit of resistance

 

The S.I. unit if resistance is Ohm (Ω).

 

What is the SI Unit of Resistivity?

 From eq(4), 

 

 

 = Ω x m^2 / m 

 

On solving we get, 

 

 

Difference Between Resistance and Resistivity

 

Relationship Between Resistivity ρ and Conductivity s

Resistivity is a measure of how well a material is at resisting the flow of current just like a frictional force while conductivity is a measure of how well a conductor allows the flow of current through it just like a water pipe. The larger is the diameter of the pipe, the larger the flow of water through it. 

 

Resistivity is the inverse of conductivity given by,

 

 

Conductivity is denoted by a symbol, ‘k or s’ and is measured in Siemens per meter