Question

show under what conditions the new resistance of a wire becomes 1 ohm if its original resistance was 4ohm

Answer 1

Answer:

Answer. Resistance is directly proportional to the length of the wire, and inversely proportional to the cross sectional area of the wire. ... Doubling the length will double the resistance, but the wire also must get thinner as it is stretched, because it will contain the same amount of metal in twice the length.

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Answer 2

Explanation:

Given: a wire of resistance 1Ωis stretched to double its length.

To find the new resistance

Here,

R=1Ω,Length=L,Cross sectional area, CSA=A

The formula used is,

R=ρ L/A

⟹ρ L/A = 1..........(i)

The new length, L =2L

And new CSA = A′

So we have,

Volume of the wire= AL

Now after the act of stretching the volume remains constant.

Therefore, AL=A′L′

⟹AL=2LA′

⟹A′ = 2A

Now the new resistance of the wire becomes

R(small new) =ρ L′/A'

⟹R (small new)

=ρ 2L/A/2

⟹R (small new) =4ρ L/A

R (small new) =4×1 by using equation (i)

Therefore the new resistance is 4Ω

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