Question

The resistance of 20m long wire is 10 ohm
if it its length is increased by 25percent
then the
new resistance will be​

Answer 1

Answer:

initial resistance, R₁  = ρ × l / A  

   

( where ρ (rho) is resistivity ; l is length of wire ; A is the area of cross section of wire)

10 Ω = ρ × l / A

(putting length of wire = 20 m )

10  = ρ × 20 / A

A = ρ × 20 / 10

A = 2 ρ    ____________________equation (1)

NOW,

 length of wire is increased by 25 %

so, new length of wire , L = $20 +(20 * \frac{25}{100} ) = 25 m$

L = 25 m

( resistivity is a constant so it will not change, length of wire is changed to become 25 m , area of cross section of wire will not change )

let, new resistance be R₂

then,

R₂ = ρ × L / A

R₂ = ρ × 25 / ( 2 ρ)               ( by eqn (1),  A =  2ρ )

R₂ = 25 / 2

R₂ = 12.5  Ω

SO , the new resistance will be 12.5 ohms.