Question

Two wires have the same resistance and radius. If the wires are made of copper and platinum with resistivities respectively of 1.70 ✕ 10−8 Ω · m and 11.0 ✕ 10−8 Ω · m, determine the ratio of their lengths.

Answer 1

L1/L2 = 6.47

Step-by-step explanation:

In order to calculate the ratio of the lengths of the wires you use the following formula for the resistivity of a wire:

`\rho=(\pi r R)/(L)` (1)

r: radius of the cross-sectional area of the wire

R: resistance of the wire

L: length of the wire

Then, you have for each wire:

`\rho_1=(\pi r_1^2R_1)/(L_1)=1.70*10^(-8)\Omega.m\\\\\rho_2=(\pi r_2^2R_2)/(L_2)=11.0*10^{10^(-8)}\Omega.m`

The resistance and radius of the wires are the same, that is, R1 = R2 = R and r1 = r2 = r. By taking into account this last and dive the equation for the wire 2 into the wire 1, you obtain:

`(\rho_2)/(\rho_1)=(11.0*10^(-8)\Omega.m)/(1.70*10^(-8)\Omega.m)=(L_1)/(L_2)\\\\(L_1)/(L_2)=6.47`

The ratio of the lengthd of the wires is L1/L2 = 6.47