Question

a 4 ohm resistance 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.

Answer 2

When the wire is doubled the length will be halved and area will be double or twice 

R = PL/A 

R1 = P(L/2) / 2A Where R1 is the new resistance 

So R1/R = {P(L/2) / 2A} / {PL/A} 

When we solve this we get  R1/R = ¼ 

=> R1 = R/4 = 4/4 = 1 OHM