Question

Determine the current flowing through an element if the charge flow is given by a. q(t)= (3e^-t -5e-^2t) nC b. q(t)= 10sin120πt pC c. q(t)= 20e^-4t cos50t µC

Answer 1

(a) The current can be found as

$$I=\text dq/\text d t,\\\space\\ I=\frac{\text d}{\text d t}(3e^{-t} -5e^{-2t})=e^{-2t}(10-3e^t)\text{ nA}.$$

(b) The current is

$$I=\text dq/\text d t,\\\space\\ I=\frac{\text d}{\text d t}[10\sin(120πt)]=1200\pi\cos(120\pi t)\text{ pA}.$$

(c) The current:

$$I=\frac{\text d}{\text d t}\Big[20e^{-4t}·\cos(50t)\Big]=\\\space\\ =-40e^{-4t}[25\sin(50t)+2\cos(50 t)]\space\mu\text{A}.$$