A 10-g piece of copper is to be formed into a wire of radius 1.0 mm at a temperature of 50 degrees C. What is the resistance of this wire? (Hint: you will need to look up the density of copper.) If a potential of 12 V is put across the wire, what is the drift velocity? (Assume one electron per copper atom)
I’ll provide you with a “road map” to answer this interesting question. Variables: R = resistance ρ = resistivity = 1.68E-8 (copper at 20?) L = length A = area D = density = 8.96 g/cm^3 = 8960 kg/m^3 V = volume R = radius of wire = 0.001 m m = mass wire = 0.010 kg ?T = temperature change (?C) α = temperature co-efficient = 0.0068 (copper) I = current (A) n = electron density = 6E28 m-3 (for copper) q = charge on electron = 1.6E-19 C Equations needed: R = ρL / A D = m / V ?R / R? = α?T I = nAvq I = V / R The length of 10 g of copper of radius 1.0 mm is calculated by: D = m / V = m / (π r? L) L = m / D π r? = (number crunching !) The resistance of 0.357 m of wire is determined by: R = ρL / A = (number crunching !) Adjusting for new temperature: ?R / R? = α?T ?R = α?T x R? = (number crunching !) Hence: R = (think & number crunching !) Drift velocity formula: I = nAvq I = V / R V / R = nAvq v = V / (nAqR) = (number crunching !) This should help. Good luck
