What do you Mean by Resistance?
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:
R is directly proportional to conductor length when temperature and other physical aspects are maintained as same.
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
The resistance of the material depends on the following factors.
It is inversely proportional to the cross-section area of the conductor.
The resistance of the material depends on its temperature.
With the increase in the length of the conductor, the resistance of the material increases.
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
Length
Shape
Nature of the material of the conductor
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
FAQs on Difference Between Resistance and Resistivity for JEE Main 2024
1. Compute the dimensional formula for electrical resistivity.
Resistivity is defined as the resistance per unit length and cross-sectional area. It is the property of the material that opposes the flow of charge or the flow of electric current.
We already know the dimensional formula for the following
R = [M1L2T-3 A-2]
L = [L1] and A = [L2]
Putting these values in eq(5) to get the dimensional formula for electrical resistivity
= [M1 L2 T-3 A-2] [L2 ]/ [L1]
The dimensional formula for electrical resistivity = [M1L-1 T-3 A-2]
2. Does resistivity increase with temperature?
Resistivity rises with the increasing temperature in conductors while decreases with increasing temperature in insulators. As the temperature rises, the number of phonons increases, because of which the electrons and photons collide. Thus, when the temperature goes up, resistance increases. Since conductors typically display an increased resistivity with temperature increases, they have a positive temperature coefficient.
In semiconductors, resistivity decreases with rising in temperature. As the temperature increases, the number of free charge carriers are increasing due to the breaking of more and more covalent bonds.
3. How do you calculate the conductance from resistance?
Since resistance R is inversely proportional to the conductance s. For example, a car is moving at a speed of 10 kmph, keeping the distance as 1 km. The time will be 1/10 hr.
It means if the resistance of the material of the conductor is 100 Ω, then the conductance will be 1/100 Ω. Here, you got another unit of conductor, and that is, ‘mho’, just the reverse of the resistance unit, ohm.
4. What is the effect of temperature on Resistance and Resistivity?
Resistance is a property of a material that opposes the flow of free electrons, whereas resistivity is the property of a material that gives the resistance for that material. The resistance and resistivity vary with variation in the temperature. The amplitude of the vibration of the atoms in the lattice increases with the increase in the temperature of the conductor. Consequently, the collision cross-section of atoms increases, thereby increasing the probability of their collision with free electrons. As a result, the resistance of a conductor increases with an increase or rise in temperature.
