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 the same temperature in time 'r'?

Step-by-step solution

Let = resistivity of the material of wire r= radius of wire Resistance of 1 ~m wire is R= 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 T= (106)^2 R t In 2^ nd case Resistance of some wire of length 2 m is : R^ = (2) r^2 = 2 r^2 =2 R and then heat is : (2 ~m ) S T = ( n )^2 t 2 R From eq. (i) and (ii) aligned n^2 200 & =2 n^2 & =400 n=20 aligned