A wire when connected to 220 V mains supply has power dissipation P 1 . Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is P 2 . The P 2 : P 1 is

Let us assume, initially Resistance of wire = R and Voltage drop acoss it=V=220 Volt

Then, P1 = V²/R

When Wire is cut down into two pieces then each wire would have resistance R/2.

Now equivalent resistance of wire connected in parallel = R/4

Then, P2= V²/(R/4)= 4V²/R = 4P1

Hence, P2:P1 = 4

P1 = V1^2/R1,

where, V=220V and R= resistance of wire.

In second case wire is cut in to 2 equal pieces  and connected in parallel so Resistance in this case is R2 =R1/2

So power P2 = V2^2/R2

P 2 : P 1 = V2^2/R2 :V1^2/R1 = R1:R2 = 2R2:R2 =2