Question

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

Answer 1

We consider wire is doubled on it means to fold the length of wire. It means 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 = 4Ω

Now, for new arrangement,

p' = p

l' = l / 2

A' = 2A

Thus,

R' = p' l'/A' = p (l /2) ÷ 2A = !/4 (p l / A)
= 1/4R = 1/4 × 4 = 1Ω.