Answer :

R = p L/A

R = 25 ohm


Volume of material in the conductor = LA

Vol of the conductor remains the same


Vol = AL

= A'L'

A' = AL/L'


After streching the wire


L' = 6L/5

A' = 5AL/6L

= 5A/6


Resistance of streched wire = R'

= pL'/A'

= p(6L/5) × {6 / (5A) }

R' = 36pL / 25A

R' = 36R / 25


Now Resistance ,


= 36×25 / 25ohm

= 36 Ohm

Hope its help you.

Calculation of New Resistance and Resistivity of a Stretched Wire

Given:
Original length of the wire, L = 1
Increase in length, ΔL = 6/5 - 1 = 1/5
Original resistance of the wire, R = 25

Calculation:
1. New Resistance:
The resistance of the wire is given by the formula, R = ρL/A, where ρ is the resistivity of the wire, L is the length of the wire and A is the cross-sectional area of the wire.

As the length of the wire is increased by 1/5 times, the new length of the wire is L + ΔL = 1 + 1/5 = 6/5

Substituting the values in the formula, we get:
R' = ρ(L + ΔL)/A

R' = ρ(6/5)/A

R' = 6ρ/5A

As the cross-sectional area of the wire remains constant, the new resistance is directly proportional to the resistivity of the wire. Thus, the new resistance can be found using the following proportion:

R/R' = ρ/ρ'

25/R' = ρ/ρ'

R' = 25ρ'/ρ

Substituting the value of R', we get:
25ρ'/ρ = 6ρ/5A

ρ' = (6ρ/5A) x (ρ/25)

ρ' = 6ρ²/125A

Thus, the new resistance of the wire is 6ρ/5A and the new resistivity of the wire is 6ρ²/125A.

2. Explanation:
When a wire is stretched, its length increases and its cross-sectional area decreases. As a result, the resistance of the wire changes. The new resistance of the wire can be calculated using the formula R' = ρ(L + ΔL)/A, where ΔL is the increase in length of the wire and A is the cross-sectional area of the wire.

The resistivity of the wire remains constant as it is a property of the material of the wire. The new resistivity of the wire can be found using the proportion R/R' = ρ/ρ', where R is the original resistance of the wire and ρ' is the new resistivity of the wire.

3. Conclusion:
In conclusion, the new resistance and resistivity of a stretched wire can be calculated using the formula R' = ρ(L + ΔL)/A and the proportion R/R' = ρ/ρ', respectively. The increase in length of the wire and the cross-sectional area of the wire should be taken into account while calculating the new resistance.