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 ${P_2}$. Then ${P_2}:{P_1}$ is
AIEEE 2002, Medium
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When wire is cut into two equal parts then power dissipated by each part is $2{P_1}$
So their parallel combination will dissipate power ${P_2} = 2{P_1} + 2{P_1} = 4{P_1}$
Which gives $\frac{{{P_2}}}{{{P_1}}} = 4$
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