In this video I go over further into linear differential equations and this time go over an example that involves the same simple electric circuit which I covered in my earlier videos on separable equations. The differential equation used to model the electric current with time through electric circuits is in fact both a linear and separable equation. My earlier video involved solving the equation using the method of separable equations. In this video I go over that same circuit but by using the more general linear equation method which I have covered in my recent videos. The resulting solution is in fact the same as that solved using the separable equation. This is a great video to illustrate how various methods of solving the same differential equation results into the same solution, so make sure to watch it!
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Application to Electric Circuits
Recall from my earlier video, https://youtu.be/E6vij-RzQ-o, in which I went over an introduction to a basic electric circuit and the differential equation to model it.
This is a first-order differential equation.
The solution gives the current I at time t.
Note that the equation is linear, as well as separable.
In my earlier video, https://youtu.be/75CyQpqbYVA, that I solved this equation as a separable equation.
In this video, I will solve it using the general method of linear equations.
Example:
Suppose that in the simple circuit shown above, the resistance is 12 Ω and the inductance is 4 H.
If the battery gives a constant voltage of 60 V and the switch is closed when t = 0 so the current I(0) = 0, find:
a) I(t)
b) The current after 1 second.
c) The limiting value of the current.
