Two wires have the same resistance and diameter. if the wires are made of platinum and gold with resistivities respectively of 11.0 ✕ 10−8 ω · m and 2.44 ✕ 10−8 ω · m, determine the ratio of their lengths.

0.222

Explanation:

The resistance of a wire is given by

where

is the resistivity

L is the length of the wire

A is the cross-sectional area

Here let's call the resistance of the platinum wire and the resistance of the gold wire. The two resistances are equal, so we can write

Where

is the resistivity of platinum

is the resistivity of gold

We know that the two wires also have same diameter, so same cross-sectional area, so

Therefore we can rewrite the equation as

And so the ratio of the lengths of the two wires is

chemical energy --> gravitational potential energy --> kinetic energy --> elastic potential energy --> gravitational potential energy

explanation:

when emma starts the hike, the chemical energy stored in her body is used to climb up the mountain, and so she gains gravitational potential energy (because at the end, she will be at a higher height h above the ground). then she goes bungee jumping: as she falls, this gravitational potential energy is converted into kinetic energy (because her speed increases as she falls down), until the point when the rope stretches, and she stops moving. at that moment, all the kinetic energy is converted into elastic potential energy due to the stretching of the rope. then, this energy is released because the rope returns to its natural length, and emma gains a small increase in altitude , so she gains some gravitational potential energy.