Question

A particular amplifying device supplies electrons in a manner such that the current passing out of the device is given by I(t) = (Io)e^kt, where I(0) = Io = 2A.The current measured 12 seconds later is 3.4 A.Find
(a)The charge Q that passes out of the device as a function of time..Q(t):
(b)The total number of electrons N that pass out of the device if left on for one minute

Answer 1

First, use the fact that I = 3.4 A at t = 12 to calculate k.
3.2 = 2.0 e^(12k)
12k = ln 1.6 = 0.47
k = 0.03917 sec^-1

(a) Integrate I(t) for Q(t), with Q = 0 at t = 0.

(b) Calculate Q(t=60) for the total charge at 1 minute, and divide by the charge of an electron, 1.6*19^-19 C,