Ten identical cells connected in series are needed to heat a wire of length one meter and radius ' r ' by 10^ C in time ' t '. How many cells will be required to heat the wirc of length two meter of the same radius by

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Correct answer: A. 20

Let = resistivity of the material of wire r= radius of wire Resistance of 1 m wire is R=( )/(π r^2) \ R=( l)/(A)\ Let =e m f of the cell in first case. All the cells are connected in series. So heat is m s Δ T=((106)^2)/(R) t In 2^ nd case Resistance of some wire of length 2 m is : R^ \ prime = ( (2))/(π r^2)=(2 )/(π r^2)=2 R and then heat is : (2 m ) S Δ T= (n) )^2 t 2 R From eq. (i) and (ii) aligned (n^2)/(200)& =2 n² & =400 n=20 aligned

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