Can someone please finish the problem. You've made the finals of the Science Olympics! As one of yourtasks, you're given 1.0 g of aluminum, that will dissipate 7.5 Wwhen connected to a 1.5 V battery. What length and diamter will youchoose for you wire? Can someone please finish the problem. You've made the finals of the Science Olympics! As one of yourtasks, you're given 1.0 g of aluminum, that will dissipate 7.5 Wwhen connected to a 1.5 V battery. What length and diamter will youchoose for you wire?
Explanation / Answer
Power P = V2/R => 7.5 = 1.52/ R Resistance ofwire R = 2.25 /7.5 = 0.300 Volume ofaluminium V = Mass/ density = 1.0 g / 2.70g/cm3 = 0.370 cm3 Also volume V = Areaof cross section * length = A *l -----------(1) Resistance R = * l / A 0.300 = 2.82 *10-6 * l /A (foraluminium = 2.82* 10-6 -cm) l /A = 0.300 / 2.82 *10-6 = 1.06 *104 ----------------(2) Multiply equation (1) and (2) l2 = 1.06* 104* 0.370 = 0.392 *104 cm length ofwire l = (0.392*104 ) = 62.6 cm Area of crosssection A = * r2 = V / l 3.14 *r2 = 0.370 /62.6 r = (18.82* 10-4) = 4.34 *10-2 cm diameter d = 2* r = 8.68 *10-2 cm