Question

A wire is gradually stretched to make it 100% longer. Its resistance will increase by ______.

Options

• 100%

• 200%

• 300%

• 400%

Answer 1

A wire is gradually stretched to make it 100% longer. Its resistance will increase by 300%.

Explanation:

When a wire is stretched, its length increases and its cross-sectional area decreases, while the volume remains constant. This affects the resistance significantly.

Let:

Initial length = l

Initial area = A

Initial resistance = R = ρ l A

Volume V = l × A (constant)

The wire is made 100% longer, so the new length:

l' = l + 100% of l

= l + l

= 2l

Since volume remains constant:

V = l × A  = l' × A'

l × A = 2l × A'

A' = `A/2`

New resistance (R') = `rho (l')/(A')`

= `rho (2 l)/(A//2)`

= `rho (4 l)/A`

= 4 R

Increase in resistance = R′ − R

= 4R − R

= 3 R

Percentage increase = `(3 R)/R xx 100%`

= 300%

∴ When a wire is stretched to double its original length, its resistance becomes 4 times, i.e., increases by 300%.