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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 the ratio (A) 2 : 1 (B) 1 : 2 (C) 16 : 1 (D) 4 : 1

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 the
ratio
(A) 2 : 1 (B) 1 : 2 (C) 16 : 1 (D) 4 : 1

Grade:

2 Answers

Arun
25763 Points
one year 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
 
Vikas TU
14149 Points
one year ago
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
 

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