Method 1 - Solving the DE

The formula is:

After substituting:

Solving:

I.F. =

When , , so

This gives us:

The transient current is: A

The steady state current is: A

Method 2: Using the Formula

NOTE: We can use this formula here only because the voltage is constant. This formula will not work with a variable voltage source.

We have:

So

In this example, the TC is

So we see that the current has reached steady state by t = 0.2 × 5 = 0.1 s

Method 3: Using Scientific Notebook's Solve ODE

If you have Scientific Notebook, proceed as follows:

This DE has an initial condition i(0) = 0. We set up a matrix with 1 column, 2 rows.

For the answer: Compute → Solve ODE... → Exact