You've made the finals of the Science Olympics! As one of your tasks, you're given 1.0 gg of aluminum and asked to make a wire, using all the aluminum, that will dissipate 6.5 WW when connected to a 2.5 VV battery.

a)- What diameter will you choose for your wire?

b)-What length will you choose for your wire?

a

The diameter is

b

The length to choose is

Explanation:

   From the question we are told that

            The mass of aluminum is  

             The expected power to dissipate is

              The potential difference is  

First we need to obtain the resistance R which is mathematically  represented as

  Substituting values

Next we obtain the volume of the aluminium which is mathematically represented as

The value of the density of aluminium is  

Now substituting the value

The resistance can also be mathematically represented as

  Where L is the length , A is the area  and is resistivity

 and for aluminum the resistivity is

Now multiplying the denominator and the numerator by L i.e

But    i.e area × length = volume

Now making L the subject of the formula in the question above

Volume can also be mathematically represented as

Now making A the subject

The area A is mathematically represented as

And  

Now substituting this into the formula for area

  Making D(diameter)  the subject of the formula

the diagram which shows forces as either balanced = same speed or unbalanced = accelerarting

b

explanation:

bc its just b