Question

A wire of uniform cross-section ‘A’ and length ‘L’ has a resistance of 4 ohm. The
wire is cut into four equal pieces, each piece is then stretched to twice the new length.
What will be resistance of each piece?

Answer 1

Answer:

Explanation:

A wire of length l and cross sectional area A has a resistance of 16Ω.

it is cut into 4 equal parts and each part is stretched uniformly to length l.

as area of each piece becomes 1/4th of A.

use formula , R = ρl/A

resistance of initial wire , R = ρl/A = 16Ω

resistance of each piece , R' = ρl'/A'

here, l' = l and A' = A/4

so, R' = ρl/(A/4) = 4(ρl/A) = 4R = 64Ω

hence, resistance of each piece of wire is 64Ω.

now all pieces are joined in parallel combination.

so, 1/Req = 1/R' + 1/R' + 1/R' + 1/R'

= 4/R'

= 4/64Ω = 1/16Ω

hence, Req = 16Ω