You are given three pieces of wire that have different shapes (dimensions). you connect each piece of wire separately to a battery. the first piece has a length l and cross-sectional area a. the second is twice as long as the first, but has the same thickness. the third is the same length as the first, but has twice the cross-sectional area. rank the wires in order of which carries the most current (has the lowest resistance) when connected to batteries with the same voltage difference. rank the wires from most current (least resistance) to least current (most resistance).

Explanation:

The resistance of a wire is given by:

where

is the resistivity of the material

L is the length of the wire

A is the cross-sectional area of the wire

1) The first wire has length L and cross-sectional area A. So, its resistance is:

2) The second wire has length twice the first one: 2L, and same thickness, A. So its resistance is

3) The third wire has length L (as the first one), but twice cross sectional area, 2A. So, its resistance is

By comparing the three expressions, we find

So, this is the ranking of the wire from most current (least resistance) to least current (most resistance).

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

i dont have a visual in front of me, but i can you reason to try to get the right one. the graph should look like this, 0 to 6 there is a spike, 12 to 14 there should be a very low point. slight increase in the graph at 12 to 14, and flat 14 to 18

explanation: