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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
25758 Points
2 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
 
Vikas TU
14149 Points
2 years 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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