Question

?a wire is stretched 30% what is the percentage change in resistance ​

Answer 1

The percentage change in resistance of the wire is 69%.

Step-by-step explanation:

Resistance of a wire can be determined by,

R = (ρl) ÷ A

Where R is its resistance, l is the length of the wire, A its cross sectional area and ρ its resistivity.

When the wire is stretched, its length and area changes but its volume and resistivity remains constant.

`l_(o)` = 1.3l, and
`A_(o)` =
`(A)/(1.3)`

So that;

`R_(o)` = (ρ
`l_(o)`) ÷
`A_(o)` = (ρ × 1.3l) ÷ (
`(A)/(1.3)`)

= (1.3lρ) ÷ (
`(A)/(1.3)`)

=
`(1.3)^(2)` × [(ρl) ÷ A]

= 1.69R (∵ R = (ρl) ÷ A)

`R_(o)` = 1.69R

Where
`R_(o)` is the new resistance,
`l_(o)` is the new length, and
`A_(o)` is the new area after stretching the wire.

The change in resistance of the wire =
`R_(o)` - R

= 1.69R - 1R

= 0.69R

The percentage change in resistance =
`(0.69R)/(R)` × 100

= 0.69 × 100

= 69%

The percentage change in resistance of the wire is 69%.