Have you ever wondered why electrical appliances heat up when used for a longer time? Resistance is a property of an electric circuit or part of a circuit that transforms electric energy into heat energy in opposing electric current. In this document, we will study about such properties as resistance and Resistivity and the effect of temperature on these in detail.
Resistance
Resistivity
In simple terms, resistance behaves differently with temperature for different materials.
However, there isn't a straightforward math formula that can describe how resistance changes with temperature for various materials, and it varies from one material to another.
When we increase the temperature, as a result the resistance increases. Suppose the resistance of a conductor at 0o C is R0 Ω increasing the temperature to C, the resistance becomes Rt Ω, as shown in fig.
Change in resistance =ΔR
ΔR = Rt  Ro
ΔR depends upon the following three factors:
1. ΔR is directly proportional to the initial resistance, Ro
2. ΔR is directly proportional to the rise in temperature, t_{0}C
3. ΔR depends upon the nature of the conductor.
Mathematically,
Where (α) is called the temperature coefficient of resistances. If the resistance of the material increases on increasing the temperature such materials have a positive temperature coefficient and when on increasing the temperature and the resistance decreases such materials have a negative temperature coefficient. From the equation, we can find
Example 1: Suppose you have a copper wire with a resistance of 10 ohms at 20 degrees Celsius. The temperature coefficient of resistance for copper is approximately 0.00393 /^{o}C. If the temperature increases to 50^{o}C, find the new resistance (Rt).
Solution: Substitute the values into the formula:
Rt =10Ω⋅(1+0.00393⋅(50−20))
Rt =10Ω⋅(1+0.00393⋅30)
R=10Ω⋅(1+0.1179)
R=10Ω⋅1.1179
R≈11.179Ω
So the new resistance Rt at 50^{o}C is 11.179Ω
Example 2: Let's say you have a sample of unknown material with a resistance of 20Ω at 25^{o}C and a resistance of 30Ω at 75^{o}C. Find the temperature coefficient of resistance (α) for this material.
Solution:
The formula for the temperature coefficient of resistance is given by:
So, the temperature coefficient of the material is 0.01 /^{o}C
The resistivity of a material is temperaturedependent. The temperature dependence of the resistivity is different for conductors, semiconductors, and insulators. Let’s discuss how resistivity varies in conductors and insulators before discussing semiconductors.
Energy Band Gaps in Materials
The resistivity of materials is dependent upon the temperature of the material.
ρ_{t} = ρ_{0} [1 + α (T – T_{0})]
is the equation that defines the connection between the temperature and the resistivity of a given material. In this equation ρ_{0} is the resistivity at an equilibrium temperature, ρ_{t} is the resistivity at t0 C, T_{0} is referred to as the reference temperature and α is the temperature coefficient of resistivity.
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1. What is the temperature dependence of resistance? 
2. What is the effect of temperature on resistance and resistivity? 
3. How does temperature affect the conductivity of a material? 
4. What is the mathematical relationship between resistance and temperature? 
5. How does the temperature dependence of resistance impact electronic devices? 

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