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 (A) 1
Let us assume, initially Resistance of wire = R and Voltage drop acoss it=V=220 Volt
Then, P1 = V^{2}/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= V^{2}/(R/4)= 4V^{2}/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