Need help with electric circuit problem?

Question

The charge entering a certain circuit element is found to be

q=5te^-10^3t.The corresponding current i=5(1-10^3t)e^-10^3t.

I need to find instant t>or = to 0 at which i is minimum, as well as i_min

pls help.. the answer is 2ms and -0.677A

Answer 1

Differentiate i with respect to time and set di/dt = 0 and solve for t.

di/dt = -5000(2 - 1000t)e^(-1000t) = 0

2 - 1000t = 0

t = .002 s

Plug t = .002 s into i(t) for i-min.

i(.002) = -.677 A