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 ?

1 Answer

#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#