The current flowing through wire depends on time as, `1 = 3t^(2) + 2t + 5`
The charge flowing through the cross - section of the wire in time `t = 0` to `t = 2` second is

Options

A. 22 C
B. 20 C
C. 18 C
D. 5 C

Answer

A

Explanation

`I=(dq)/(dt)=3t^(2)+2t+5 therefore dq=(3t^(2)+2t+5)dt`
`therefore q=underset(t=0)overset(t=2s)int(3t^(2)+2t+5)dt`
`=(3t^(3))/(3)+(2t^(2))/(2)+5t|._(0)^(2)=t^(3)+t^(2)+5t|_(0)^(2)`
`=2^(3)+2^(2)+5xx2-0=8+4+10=22C`