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Question: Calculate the area of cross section of a wire of length 2m, resistance \(46{\text{ }}\Omega \) and r...

Calculate the area of cross section of a wire of length 2m, resistance 46 Ω46{\text{ }}\Omega and resistivity 1.84×10−6Ωm1.84 \times {10^{ - 6}}\Omega {\text{m}}.

Explanation

Solution

In this question we have to find the area of cross section of wire having length equal to 2m, resistance 46 Ω46{\text{ }}\Omega and resistivity 1.84×10−6Ωm1.84 \times {10^{ - 6}}\Omega {\text{m}}. To find the cross section we are going to use the formula of resistivity.

Complete step by step solution:
Given,
Length L = 2m
Resistance R =46 Ω46{\text{ }}\Omega
Resistivity ρ\rho =1.84×10−6Ωm1.84 \times {10^{ - 6}}\Omega {\text{m}}
Formula of resistivity is given below,
R=ρLAR = \dfrac{{\rho L}}{A}
To find the value of A, putting the values of R, L and ρ\rho
⇒A=ρLR\Rightarrow A = \dfrac{{\rho L}}{R}
⇒A=1.84×10−6×246\Rightarrow A = \dfrac{{1.84 \times {{10}^{ - 6}} \times 2}}{{46}}
⇒A=3.68×10−646\Rightarrow A = \dfrac{{3.68 \times {{10}^{ - 6}}}}{{46}}
⇒A=0.08×10−6 m2\Rightarrow A = 0.08 \times {10^{ - 6}}{\text{ }}{{\text{m}}^2}

Hence from above calculation we can see that the value of cross section of the wire is A=0.08×10−6 m2A = 0.08 \times {10^{ - 6}}{\text{ }}{{\text{m}}^2}.

Note: In this question, we have used the formula of resistivity ρ\rho . Now we are going to understand more about resistivity. Resistivity of a wire is electrical resistance of that wire per unit cross sectional area and per unit length.
Resistivity is a property of the material of that wire. Resistivity has various applications in electronics. Resistivity is useful to compare metals, on the basis of their ability to conduct electric currents through them. High resistivity shows poor conductivity of that metal and low resistivity shows high conductivity of that metal. The unit of resistivity is Ωm\Omega m. The opposite of resistivity is conductivity. It shows how easily the current can and heat flow through that metal. The unit of conductivity is Ωm−1\Omega {m^{ - 1}}. It is also a measure to compare properties of different metals. There are some other types of conductivity also –
(a) The electrical conductivity of an electrolyte in solution is called Electrolytic conductivity.
(b) The conductivity due to ions moving in a crystal lattice is called Ionic conductivity.
(c) It is a property of a porous material’s ability to transmit water is called Hydraulic conductivity.
(d) The thermal conductivity of a material is its ability to conduct heat.