Question

A 16 Ω resistance wire is doubled on it. Calculate the new resistance of the wire.

Answer 1

Explanation:

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.