Youve made the finals of the Science Olympics! Asone of your tasks, youre given
ID: 1756204 • Letter: Y
Question
Youve made the finals of the Science Olympics! Asone of your tasks, youre given 0.74 g of aluminum and asked to makea wire, using all the aluminum, that will dissipate 6.62 W whenconnected to a 1.1 V battery. What length will you choose for yourwire? What diameter will you choose for yourwire? Youve made the finals of the Science Olympics! Asone of your tasks, youre given 0.74 g of aluminum and asked to makea wire, using all the aluminum, that will dissipate 6.62 W whenconnected to a 1.1 V battery. What length will you choose for yourwire? What diameter will you choose for yourwire?Explanation / Answer
first, we need to find the required resistance of the wire: V=I*R P=V*I P=V*(V/R) 6.62=1.12/R R=.183 the resistivity of aluminum is 2.65E-8 *m the equation is: R=*L/A=*L/(d2/4), where is theresitivity. we also have a constraint on the amount of material (.74g ofaluminum): =m/V 2700=.00074/V V=2.74E-7 m3=L*(d2/4) since we have 2 equations and 2 unknowns, we can substitute andsolve: .183=2.65E-8*L/(d2/4) 2.74E-7 m3=L*(d2/4) I think you can do the algebra yourself, but the answer you shouldget is: L=1.38m d=.000504 m
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