Question

Find the charge q(t) flowing through a device if the current is:

a. I(t) = 2t^2
b. I(t) = sin(t)
c. I(t) = e^t
d. I(t) = cos(t)

Answer 1

To find the charge q(t) over time for the given current I(t) equations, one must integrate I(t) with respect to time, with the constant of integration C determined based on initial conditions or boundary conditions.

Step-by-step explanation:

The student is asking about finding the charge q(t) as a function of time given different current I(t) equations. To find q(t), we integrate the current with respect to time. Let's apply this approach to each part:

1. For I(t) = 2t^2, we integrate to get q(t) = (2/3)t^3 + C, where C is the constant of integration.
2. For I(t) = sin(t), we integrate to get q(t) = -cos(t) + C.
3. For I(t) = e^t, the integration yields q(t) = e^t + C.
4. Finally, for I(t) = cos(t), we integrate to get q(t) = sin(t) + C.

Note that C represents the initial charge at t=0 or another point that the boundary condition specifies.