The correct relationship between P and P1 can be determined by examining the factors that contribute to power dissipation in a metallic wire. Power dissipation in a wire is given by the equation P = (V^2) / R, where V is the voltage applied across the wire and R is its resistance.

Comparing wire A and wire B, we can see that wire B has twice the radius and twice the length of wire A. The resistance of a wire is inversely proportional to its cross-sectional area, which is proportional to the square of its radius. Therefore, the resistance of wire B is (2r)^2/(r^2) = 4.

Now, considering the equation for power dissipation, we can see that the resistance of wire B is four times that of wire A. When the same voltage V is applied across both wires, the power dissipated in wire B will be one-fourth (1/4) that of wire A. Hence, the correct relationship is P = P1/2.

Therefore, option 2 (P = P1/2) is the correct answer.