resistance of each part=4/4=1ohm..since these four r joined in parallel.....so equivalent resistance =R=r/4=1/4=0.25.....therefore answer is 0.25 ohm...

Introduction:
In this question, we are given a wire of uniform cross-section and length 'l' with a resistance of 4 ohms. The wire is then cut into four equal pieces, each of which is stretched to length 'l'. Finally, these four wires are joined together in parallel. We need to calculate the new resistance of the combined wires.

Calculating the resistance of a wire:
The resistance of a wire can be calculated using the formula: R = ρ * (L/A), where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

Resistance of the original wire:
Given that the original wire has a resistance of 4 ohms, we can use the formula to find its resistivity. Rearranging the formula, we get: ρ = R * (A/L).

Equal pieces of wire:
When the original wire is cut into four equal pieces, each piece will have a length of 'l/4'. Since the length of each piece is reduced, the resistance of each piece will increase. However, the cross-sectional area remains the same as the wire is uniform.

Stretched wires:
Each of the four pieces is then stretched to length 'l'. Stretching the wire does not change the resistivity of the material. The length of each wire is now 'l', and the cross-sectional area remains the same.

Joining wires in parallel:
When the four wires are joined in parallel, the total resistance of the combination can be calculated using the formula: 1/R_total = 1/R1 + 1/R2 + 1/R3 + 1/R4.

Calculating the new resistance:
Let's assume the resistance of each stretched wire is R'. Since the original wire was cut into four equal pieces, each piece will have the same resistance. So, R' = R/4.

Substituting the values into the parallel resistance formula:
1/R_total = 1/R' + 1/R' + 1/R' + 1/R'
1/R_total = 4/R'
1/R_total = 4/(R/4)
1/R_total = 16/R
R_total = R/16

Therefore, the new resistance of the combined wires is R/16 = 4/16 = 0.25 ohms.

Conclusion:
The new resistance of the combined wires, when cut into four equal pieces and joined in parallel, is 0.25 ohms. This decrease in resistance is due to the increase in the number of pathways for the current to flow, resulting in an overall decrease in resistance.