## Relation between resistance and temperature | Rt = Ro (1 + 𝛼ΔT)

### Relation between resistance and temperature | Rt = Ro (1 + 𝛼ΔT)

Thursday, 24 December 2020

Every student must hear these two words in class 10. Both resistance and temperature are of different meaning. But as the point of physics both the terms are interconnected to each other. Means both resistance and temperature have relation between them. So here we will find the mathematical relation between resistance and temperature.

In electric current and circuit, we already study about electric current and circuit. As we know when electric current flows through a conducting wire some electricity losses during flow of electrons. this is because of the converting of electric energy into heat energy. During the flow of current through wire Some forces oppose the flow of electrons (known as resistance of wire. more opposition means more resistance or less opposition means less resistance) and due to this opposition heat energy generated means temperature increases. Hence just because of this phenomena there exist a unique relationship between resistance and temperature.

As we discuss when electric current flows through a conducting wire, the wire oppose the flow of electron know as resistance and due to this opposition temperature of the conductor increases. Hence there must be some connection between resistance and temperature. So lets go further to find the relationship between temperature and resistance. we will also derive this relation for better understanding.

## Relationship between resistance and temperature

The mathematical relationship between resistance and temperature is Rt = Ro (1 + 𝛼ΔT). Means final resistance is equal to the product of initial resistance and one added with the coefficient of resistivity multiplied by change in temperature.

The formula of relation between resistance and temperature is Rt = Ro (1 + 𝛼ΔT).

These are some common relation between resistance and temperature.
• On increasing the temperature of the conductor the resistance of the conductor also increases. Hence we can say that there is a direct relation between resistance and temperature.
• Similarly on decreasing the resistance of the conductor the temperature also decreases.

Please note that a highly resistance wire heat up faster than a low resistance wire. So it should be right to use low resistance wire in our home. fuse wire is low resistance wire that means its temperature is also low.

Hence, as we know the formula of relation between resistance and temperature is Rt = Ro (1 + 𝛼ΔT).

Where,

Rt is final resistance,

Ro is initial resistance,

𝛼 is thermal or mean coefficient of resistivity or coefficient of resistivity.

ΔT = (Tf - Ti) or change in temperature.

Example:-

If the resistance of the conductor is 5 Ω at 50°C and 7 Ω  at 100°C, then the mean temperature coefficient of resistivity of the material is:

Rt = 7 Ω  at 100°C

Ro = 5 Ω at 50°C

ΔT = (Tf - Ti) = (100 - 50) = 50°C

Now,

Rt = Ro (1 + 𝛼ΔT)

7 Ω = 5 Ω (1 + 𝛼 ✕ 50°C)

𝛼 =  (7 Ω /  5 Ω - 1 ) / 50

𝛼 = 2 Ω / (5 Ω ✕ 50)

𝛼 = 2 / 250

𝛼 = 0.08