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  4. A wire when connected to 220 V mains supply has power dissipation P1. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is P2 then P2: P1 is

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Q. 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

AMUAMU 2015Current Electricity

Solution:

When wire of resistance say R is cut into two pieces, its resistance becomes half i.e. R /2. Here equivalent resistance
$R_{eq} = \frac{1}{2} \frac{R}{2} = \frac{R}{4}$
$\therefore $ $P_2 = \frac{V^2}{R/4} = 4 \frac{V^2}{R} = 4P_1$
or $P_2 : P_1 = 4$

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