Question

the resistance of a wire of length 250 metre is 1 ohm if the resistivity is 1.6 in to 10 to the power minus 8 ohm metre find the area of cross section so how much does the resistance to change if the diameter is doubled.

Answer 1

The information provided in the question is as follows:

Length of wire, l	250 m
Resistance of wire, R	1 Ω
Resistivity of wire, ρ	1.6×10-8 Ω m

$$\begin{gathered} Theresis\tan ceisgivenas: \\ R=\rho \frac{l}{A} \\ \Rightarrow 1=1.6\times {10}^{-8}\times \frac{250}{A} \\ \Rightarrow A=1.6\times {10}^{-8}\times 250=4\times {10}^{-6}{\text{m}}^2 \\ \text{A=π}{\left(\frac{d}{2}\right)}^2 \\ \text{When the diameter is doubled, then} \\ A\text{'}=\pi {\left(\frac{d\text{'}}{2}\right)}^2=\pi {\left(\frac{2d}{2}\right)}^2=4\pi {\left(\frac{d}{2}\right)}^2=4A \\ Keepingthesamelength,theresis\tan ceofthewire, \\ R\text{'}=\rho \frac{l}{A\text{'}}=\frac{1}{4}\rho \frac{l}{A}=\frac{R}{4}=\frac{1}{4}=0.25\Omega \end{gathered}$$