# A current flowing through a wire depends on time as I = 3t2 + 2t + 5. The charge flowing through the cross section of the wire in time from t = 0 to t = 2 sec is: (a) 22 C (b) 20 C (c) 18 C (d) 5 C

Given

I = 3t2 + 2t + 5

Time interval t = 0 and t = 2 sec

We know that,

I = dq/dt

Therefore,

$\int&space;dq&space;=&space;\int_{0}^{2}I&space;dt$

$q&space;=&space;\int_{0}^{2}(3t^{2}+2t+5)dt$

$q&space;=&space;\left&space;[&space;t^{3}+t^{2}+5t\right&space;]_{0}^{2}$

We get,

q = (8 + 4 + 10)

q = 22 C

Therefore, the correct option is (a)