Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires is lighter? Hence explain why aluminium wires are preferred for overhead power cables. (ρAl = 2.63 × 10–8 Ω m, ρCu = 1.72 × 10–8 Ω m, Relative density of Al = 2.7, of Cu = 8.9.)
Given: For aluminium: d1=2.7,ρAl=2.63×10−8Ω m, mass =m1, Area =A1 For copper: d2=8.9,ρCu=1.72×10−8Ω m, mass =m2, Area =A2 Step 1: Resistance of two wires As length of both wires is same, say ℓ. For aluminium, R1=ρAlA1ℓ ...........(1) For copper, R2=ρCuA2ℓ ...........(2) As given, R1=R2 From Equations (1) and (2) ⇒A2A1=ρCuρAl ..........(3) Step 2: Mass of two wires For aluminium: m1=A1ℓd1 ..........(4) For copper: m2=A2ℓd2 ..........(5) Step 3: Ratio of masses of wires Equation (4)÷(5) m2m1=A2A1d2d1 Put the value of A2A1 from eq. (3) m2m1=ρCuρAld2d1 ..........(6) Step 4: Substituting all the values in eq. (6) m2m1=1.72×10−82.63×10−8×8.92.7 m2m1=0.4638 ...........(7) Step 5: From equation (7) we can say that mass of aluminum wire(m1), is less than mass of copper wire(m2). Hence aluminum is lighter than copper. Since aluminum is lighter, it is preferred for overhead power cables over copper.
