We define 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.

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).

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

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 on 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.

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) m^2 and that of L is meter(m).

SI unit of resistance

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

From eq(4),

= Ω x m^2 / m

On solving we get,

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

(S /m).

FAQ (Frequently Asked Questions)

1. Compute the dimensional formula for electrical resistivity.

We already know the dimensional formula for the following

R = [M^{1}L ^{2}T ^{-3} A^{-2}]

L = [L^{1}] and A = [L^{2} ]

Putting these values in eq(5) to get the dimensional formula for electrical resistivity

= [M^{1} L ^{2}T ^{-3} A^{-2}] [L^{2} ]/ [L^{1}]

The dimensional formula for electrical resistivity = [M^{1}L^{-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.

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.