A 4-ohm resistance wire is doubled on it calculate the new resistance of the wire.

First consider that wire is doubled on it means to fold the length of wire. That is its length will get half and area of cross-section will get doubled.

∴ Let the resistance of the wire originally ‘R’ of length ‘L’ and area of cross-section ‘A’ with resistivity of material is ‘p’, Then

R = p l/A = 4 Ω

Now, for new arrangement,

p’ = p

l’ = l / 2

A’ = 2A

Thus,

R’ = p’ l’/A’ = p (l /2) ÷ 2A

= 1/4 (p l / A)

= 1/4R

= 1/4 × 4

= 1Ω.

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