Question

two conducting wires of same materialand of equal lengths, resistance, and resistivity having ratio 1:2. their diameter ratio will be------a) 1:2 b) 1:4 c) 4:1 d) 1:square root of 2
Pls give solution tooo

Answer 1

ANSWER.....

THERE DIAMETERS RATIO WILL BE... 4:1

SOLUTION :--

R1=1/area
R2=1/area

R1/R2=πr2^2/πr1^2

R1/R2=4:1


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Answer 2

Answer:  d) 1/√2

Explanation:

Let the resistivity of first wire is ρ₁ and of second wirte is  ρ₂

Given,

ρ₁/ρ₂ = 1/2

Now,

We know that,

resistivity of a wirre is directly proportional to its cross section area.

If the cross section area of wires are A₁ and A₂ respectively,

ρ₁/ρ₂ = A₁/A₂

A₁/A₂ = 1/2

If the radius of wires are r₁ and r₂ respectively,

A₁  = πr₁²

A₂ =  πr₂²

A₁/A₂ = r₁²/r₂²

1/2  = r₁²/r₂²

r₁/r₂ = 1/√2

Ratio Of diameter:-

D₁/D₂ = 2r₁/2r₂

D₁/D₂ = 1/√2

Hence, Option d) is correct.

Note:- There is a conflict in  the question. It is given in the question that both wire are made of same material ; On other hand its given that ratio of their resistivity is 1:2 Which is not possible. Resistivity of same material should be same