Question

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??

Answer 1

`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`