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Question: A wire \(l = 8\,m\) long of uniform cross-sectional area \[A = 8\,m{m^2}\], has a conductance of \[G...

A wire l=8 ml = 8\,m long of uniform cross-sectional area A=8 mm2A = 8\,m{m^2}, has a conductance of G=2.45 Ω−1G = 2.45\,{\Omega ^{ - 1}} . The resistivity of the material of the wire will be?
A. 2.1×10−7s2.1 \times {10^{ - 7}}s
B. 3.1×10−7s3.1 \times {10^{ - 7}}s
C. 4.1×10−7s4.1 \times {10^{ - 7}}s
D. 5.1×10−7s5.1 \times {10^{ - 7}}s

Explanation

Solution

The resistivity formula is used here. The electrical resistance of an object is a measure of its resistance to the flow of electric current in electronics and electromagnetism. Electrical conductance is the ease with which an electric current flows in the reciprocal quantity.

Formula used:
R=ρlAR = \rho \dfrac{l}{A}
Here, ρ\rho = resistivity, RR= resistance, LL = length and AA = area.

Complete step by step answer:
An object's resistance is mostly determined by the material it is constructed of. Electrical insulators, such as rubber, have a very high resistance and low conductivity, whereas electrical conductors, such as metals, have a very low resistance and great conductivity.

Resistivity or conductivity are used to measure this connection. Resistance and conductance are not only determined by the nature of a material; they are also influenced by the size and shape of an item, as these qualities are widespread rather than intensive. The resistance of a wire, for example, is higher when it is long and thin, and lower when it is short and thick.

Given, a wire l = 8 m long of uniform cross-sectional area A=8mm2A = 8m{m^2}, has a conductance of G=2.45Ω−1G = 2.45{\Omega ^{ - 1}}. The resistivity of material of the wire will be
R=ρlAR = \rho \dfrac{l}{A}
⇒G=1R\Rightarrow G = \dfrac{1}{R}
Hence ρ=AGl\rho = \dfrac{A}{{Gl}}
ρ=8×10−62.45×8\rho = \dfrac{{8 \times {{10}^{ - 6}}}}{{2.45 \times 8}}
∴ρ=4.1×10−7s\therefore \rho = 4.1 \times {10^{ - 7}}s

Hence option C is correct.

Note: One should not get confused that resistivity depends on length and area of the cross-section. It is independent of length and cross section area. The resistivity is the property of the material which depends on the nature and the composition of the material and the composition is affected by the temperature. Hence, the resistivity depends on the temperature. Never forget to mention the unit which is semens.