# A wire of resistance R, length l and uniform area of cross-section A is stretched till its length becomes double. It is then cut into three pieces of equal length which are connected in parallel. Find the net resistance of the combination in terms of the resistance R.|

Given,
Resistance = R
length = l
Area of cross section = A
when the wire is stretched to 2l
length become = 2l
Area of the cross-section will be A/2
The new resistance of wire
$R_{n}= 4R$
then the wire is cut into three-piece of the same length
then the new length of each piece $= \frac{l}{3}$
then Resistance of each piece $= \frac{R_{n}}{3}= \frac{4}{3}R$
When three such resistance are connected in parallel

Net Resistance $= \frac{4}{9}R$

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