Two copper wires of the same gauge one has a length L and th

Two copper wires of the same gauge, one has a length L and the other twice that. If the first wire has a resistance R, what is the resistance of the second wire? What can be said of the relationship between resistance and length? Two copper wires have the same length. The first has a cross-sectional area os A, while the second has twice that. If the first wire has a resistance R, what is the resistance of the second wire? What can be said of the relationship between resistance and cross-sectional area? The instructions for an electric hedge clipper suggest that a 20-gauge cord with a cross-sectional area of 5.2 times 10^-7m^2 extension cord can be used for distances up to 35m, but a thicker 16-gauge with a cross sectional area of13 times 10^-7 m^2 cord should be used for longer distances, to keep the resistance of the wire as small as possible. Determine the resistance of 35m of 20-gauge copper wire. Determine the resistance of the same 20-gauge copper wire, but change the length to 70m. How do the two resistances compare? Determine the resistance of 16-gauge copper wire with a length of 35m. Determine the resistance of 16-gauge copper wire with a length of 35m, but with an area of 5.2 x 10^7m^2. How do the two resistances compare?

Solution

Questions.
1. R = (rho)l/A
so new R = 2R
linear relation

2. R = (rho)l/A
new R = R/2
inverse relation

Excercises:

1. 20 gauge = 5.2810^-7 m^2
R = 1.68*10^-8 35/5.2*10^-7 = 1.1134 Ohms
2. R = 1.1134*2 = 2.2268 Ohms
This is the double of the previous
3. 16 gauge = 13*10^-7 m^2
R = 1.68*10^-8 * 35/13*10^-7 = 0.452 Ohms
4. R = 2.2268 Ohms
More than previous, same as the 20 gauge, 70m long wre