Question

The current through a wire depends on the time as, i=(10+4t) . Here, i is in ampere t in seconds. find the charge crossed through a section in time interval between t=0 to t=10 sec ?

Answer 1

`300`

Explanation:

The electric current `I=10+4t` , the rate of flow of charge `I={dQ}/dt`, is the function of time then the charge crossed in differential time `dt` is given as follows

`dQ=I\ dt`

Now, integrating above equation from `t=0` to `t=10\ sec`, we get the total charge crossed in given time interval

`Q=\int_0^Q\ dQ=\int_0^10 Idt`

`Q=\int_0^10(10+4t)\ dt`

`=(10t+2t^2)_0^10`

`=10\cdot 10+2\cdot 10^2`

`=300`