One Kg of copper is drawn into a wire of 1mm diameter and a wire of 2 mm diameter. The resistance of the two wires will be in theratio(A) 2 : 1 (B) 1 : 2 (C) 16 : 1 (D) 4 : 1
aniket anand , 11 Years ago
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2 Answers
Arun
Last Activity: 4 Years ago
Let r1 and r2 be the resistance of two wires. Let l1 and l2 be the lengthsand density be d. As mass of copper =1kg is same for both wires, mass of first wire=mass of second wire. volumexdensity of first wire = volume x density of second wire. v1xd=v2xd2(πr1² l₁) x d = (π r2² l₂)xdl₁/l₂=(r₂/r₁)² ----- equation 1 now ratio of resistances of two wires R1/R2₂= (ρ l₁/A₁)/(ρ l₂/A₂) =(A₂/A₁) x l₁/l₂ =(πr₂²/πr₁² )x (r₂/r₁) ² --------------[from equation 1] =(r₂/r₁)⁴ =(2/1)⁴ =16: 1 so, the ratio of new resistances of wires will be 16:1 therefore, R1/R2=16/1 R1=16R2