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Pavlova-9 [17]
3 years ago
15

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.
Physics
1 answer:
Zolol [24]3 years ago
3 0

Answer:

L1/L2 = 6.47

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=\frac{\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=\frac{\pi r_1^2R_1}{L_1}=1.70*10^{-8}\Omega.m\\\\\rho_2=\frac{\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:

\frac{\rho_2}{\rho_1}=\frac{11.0*10^{-8}\Omega.m}{1.70*10^{-8}\Omega.m}=\frac{L_1}{L_2}\\\\\frac{L_1}{L_2}=6.47

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

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