**resistance and resistivity**,

**their units**,

**formulae**,

**factors affecting resistance**, and

**numerical examples**.

# What is Resistance?

The measure of opposition offered by a substance in the flow
of electric current (or electrons or electric charge) is called the **resistance **of the substance. The **electrical resistance** is sometimes also
called **electrical friction**, it is
because it causes restricts the motion of charge and results in the production
of heat in the substance. The resistance of a material is denoted by the symbol
*R* and is measured in **ohm (****Ω)**. The unit of resistance “Ohm” was named in the
honor of **German physicist Georg Simon
Ohm**.

The empirical **formula
of the resistance** is given by,

Where, *ρ* is the resistivity or specific
resistance of the material, *l* is the
length of the material (or conductor) and *A*
is the area of cross-section.

## How does Resistance Oppose the Flow of Current?

From the definition of electric current, we know that electric current
is the flow of electric charge or **free electrons**.
The amount of friction or opposition that a material offers to the flow of free
electrons is the resistance of the material. When these free electrons pass
through the material, atoms and molecules of the material obstruct the flow of
these free electrons. More specifically, we can say that the free electrons
flowing through a substance collide with its atoms and molecules. On each
collision, these electrons lose some part of their energy and stop to flow
through the substance. In this way, the resistance of the material opposes the
flow of electric current through it. As we discussed earlier, resistance is
the electric friction that a material offers in the current flow and causes the production
of heat in the material with the flow of electric current. This heat is a
result of the collision of moving free electrons with the atoms and molecules of
the material.

## Unit of Resistance

The
practical unit of resistance is **Ohm**
and it is represented by the Greek letter **omega
(Ω)**. The one ohm may be defined as under-

*A conductor wire is said to have an
electrical resistance of 1 ohm if a potential difference or voltage of 1 volt
across the end of a conductor causes a current of 1 ampere to flow through it*.

# What is Resistivity?

The
property of a material by virtue of which it opposes the flow of electric charge or
electrons or electric current through it, is known as the **resistivity** of the material. The resistivity of a material is also
known as **specific resistance**. The
value of resistivity depends upon the nature of the material. It is denoted by the
Greek letter rho (*ρ*). Resistivity
is the property that creates opposition in the flow of current. From equation (1), we can write the expression of the resistivity as,

If
in equation (2), *A = 1* m^{2}
and *l = 1* m, then *ρ = R*. Therefore, the resistivity or
specific resistance of a material is the resistance offered by 1 meter length
of wire of the material having a cross-sectional area of 1 m^{2}.

From
equation (2), we may also derive the **unit
of resistivity or specific resistance** as,

Thus,
the unit of resistivity is **ohm-meter**
or **Ω-m**.

# Factors Affecting Resistance

From equation (1), we can state that the resistance *R* of a conductor-

- Is
directly proportional to its length (
*l*). - Is
inversely proportional to its area of cross-section (
*a*). - Depends on the nature of the material, i.e. resistivity of the material.
- Changes with the temperature.

Therefore,
if there are two conductors of different lengths, then the conductor with a longer length will have higher electrical resistance because the resistance
increases with an increase in the length of the conductor. On the other hand, the
conductor having a larger cross-section area will have lower electrical resistance
because the resistance is in inverse relation to the area of the cross-section. Also,
the change in the temperature of the conductor greatly influences the
resistance of the conductor.

Hence,
in practice when we need a wire to carry a large amount of current, we use a
thick wire, i.e. a wire having a large area of cross-section so it offers very
low resistance and hence causes low power loss in the form of heat.

# Effect of Temperature on Resistance

As
we discussed in the above section that the electrical resistance of material
changes with the variation in its temperature. This **effect of temperature on the electrical resistance** of the material varies
according to the type of material which is discussed in the following sections-

**Effect of temperature on resistance of pure metals**– The electrical resistance of pure metals like aluminium, silver, copper, etc. increases with the increase of temperature. Therefore, pure metals have a**positive temperature coefficient of resistance**. The change in the resistance of pure metals is fairly regular for normal ranges of temperature, consequently, the graph plotted between resistance and temperature for metal is a straight line. Practically, when the temperature of metals increases, free electrons in metals start accelerating and colliding more frequently with atoms and molecules of the material. In this way, the increased collisions result in an increase in the resistance of metals.**Effect of temperature on resistance of insulators, electrolytes, and semiconductors**– The electrical resistance of insulators, electrolytes, and semiconductors decreases with the increase in temperature. Therefore, the insulators, electrolytes, and semiconductors have a**negative temperature coefficient of resistance**. Practically, the resistance of these materials decreases because the increase in temperature releases more free electrons and holes or ions in these materials that increase the conductivity of materials. Consequently, the resistance of these materials decreases with the increase in temperature.**Effect of temperature on resistance of alloys**– The electrical resistance of alloys increases with the increase in temperature. Hence, alloys also have a**positive temperature coefficient of resistance**. Although, this increase is very small and irregular. As a result, we can say that the change in resistance of alloys is practically negligible over a wide range of temperatures.

**Numerical Example (1)** – A copper wire of 1600 m in length
has an area of cross-section of 0.12 mm^{2}. If the resistivity of
the copper wire is 0.02 µΩ-m. Then, find the resistance of the copper wire.

**Solution** – Given data,

`\l=1600" m"`

`\A=0.12" mm"^2=0.12×10^(-6)" m"^2`

`\ρ=0.02" μΩm"=0.02×10^(-6)" Ωm"`

Therefore,
the resistance of the given copper wire will be

**Numerical Example (2)** – Find the specific resistance of a
material. If a wire of the material is 3 m long and has an area of cross-section
of 2.5 mm^{2}, and possesses an electrical resistance of 200 ohms.

**Solution** – Given data,

The
specific resistance or resistivity of the material of the given wire is

# Conclusion

Hence,
in this article, we discussed electrical resistance and resistivity,
their unit of measurement, and their formula. Also, we discussed how the electrical
resistance opposes the flow of electric current and the effect of temperature on
the resistance of different types of materials.

# Video Tutorial

You can also watch the following video to understand the concept of resistance.

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