The current in conductor varies with time `t` as `I = 2 t + 3 t^(2)` where `I` is in ampere and `t` in seconds. Electric charge flowing through a section of the conductor during `t = 2 sec` to `t = 3 sec` is

Options

A. `10 C`
B. `24 C`
C. `33 C`
D. `44 C`

Answer

B

Explanation

(b) `dQ = Idt implies Q = int_(t = 2)^(t = 3) Idt = [ 2 int_(2)^(3) tdt + 3 int_(2)^(3) t^(2) dt]`
`= [t^(2)]_(2)^(3) + [t^(3)]_(2)^(3) = (9 - 4) + (27 - 8) = 5 + 19 = 24 C`.