If a wire of resistance R is melted and recast to half of its length then the new resistance of the wire will be
R/4, refer to the formula; R= pL/A, where p is resistivity and L is it's length and A being the area.
The new area is twice the previous one and length is half, so the new resistance becomes R/4.
2R
Its new resistance is R
To find the new resistance of the wire after it is melted and recast to half of its length, we can use the formula for resistance: 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.
Let's assume that the initial length of the wire is L_1, and its resistance is R_1. After melting and recasting the wire to half of its length, the new length of the wire would be L_1/2.
However, the cross-sectional area of the wire remains unchanged when it is melted and recast. Therefore, the new resistance, R_2, can be calculated as:
R_2 = ρ * (L_1/2) / A
Since the resistivity and cross-sectional area remain the same, we can simplify the equation to:
R_2 = (1/2) * R_1
So, the new resistance of the wire will be half of its initial resistance.