Test: Factors affecting Resistivity & Power(13 Nov) - JEE MCQ

The typical range of resistivity for metals is from 10⁻⁸Ωm to 10⁻⁶Ωm

Here, R₀ = 99Ω, T₀ = 27^∘C
R_T = 116Ω;
α = 1.710^−4∘C⁻¹
∴ R_T = R₀ [1 + α(T − T₀)]
∴ R_TR₀ − 1 = α(T − T₀)
⇒ 11699 − 1= α(T − T₀)

= 
∴
⇒ T = 1010.1 + T₀ = 1010.1 + 27

= 1037.1^∘C

Here, T₁ = 27^∘C, R₁ = 65Ω
R₂
= Supply voltage / Steady current
= 220 / 2.8
= 78.6Ω
Now, using the relation
R₂ = R₁[1 + α(T₂ − T₁)]
∴ 

T₂ − T₁ = 1231
T₂ = 1231 + T₁ = 1231 + 27
= 1258C^∘

Metals, including alloys, have free electrons as charge carriers. Their movement controls by defects. One of defects of usual metal is oscillations of atoms due to temperature. More temperature - more oscillations - more collisions of electrons with atoms - less mobility - more resistivity. In alloys, like constantan, atoms are in disorder so alloys have big resistivity. Their additional disorder due to temperature increase is insignificant. That is why alloys have no temperature dependence of resistivity. The same picture is with metal glasses.

In conductors due to increasein temperature the resistivity increases and in semiconductors if the decreases exponentially.

Here, R₁ = 2.5Ω, T₁ = 28^∘C
R₂ = 2.9Ω and T₂ = 100^∘C
As R₂ = R₁[1 + α(T₂ − T₁)]
∴ 2.9 = 2.5[1 + α(100 − 28)]

= 
= 2.22 × 10^−3∘C⁻¹

Here,R₀ = 5Ω, R₁₀₀ = 5.25Ω, R_t = 5.5Ω
As,R₁ = R₀(1 + αt)
∴R₁₀₀ = R₀(1 + α100)

Equation (i) and (ii), we get

= 200^oC

Human body has different resistances, when dry, resistance is 100,000 ohms. When wet because of sweat or water, resistance is only 1,000 ohms.

Wire bound resistors are made by winding the wires of an alloy, viz. manganin, constantan, nichrome etc. The choice of these materials is dictated mostly by the fact that their resistivities are relatively insensitive to temperature. These resistances are typically in range of a fraction of an ohm to a few hundred ohms.