Ten identical cells connected in series are needed to heat a wire of length 1 m and radius r by 10°C in time t. How many cells will be required to heat the wire of length 2 m of same radius by the same temperature in time t??

1 Answer
Jan 31, 2018

20

Explanation:

Suppose, 10 identical cells each had voltage of V,so in series,total voltage will be 10V

Now, resistance(R) is directly proportional to the length(l),so as length is doubled,resistance will also become doubled.(ref. R prop l/A)

So,we can say,Heat generated =( V^2/R) *t ,which will be taken up by the wire, So, we can write, (V^2/R)*t = ms del theta(where,m is the mass of the wire, s is specific heat and del theta is the increase in temperature)

Again,mass is directly proportional to length.(ref. mass =volumedensity= lengtharea*density)

So, for the initial case,we can write,

(10V)^2/R *t = ms del theta...1

and,finally after the changes made,if we need n cells,then,

(nV)^2/(2R)*t = (2m)s del theta....2

putting the value of ms del theta in equation 2 from 1,we get, n=20