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Applications of Differential Equations

Electric Circuits

Exercises to Work by Yourself

Exercise B

(continued from last page...)

Now let's look at a case where the electromotive force is no longer zero! In fact assume the following parameters:

  • inductance of 5 henrys
  • resistance of 0 ohms
  • capacitance of 0.01 farads

With initial conditions:

  • I(0) = 0 amperes
  • q(0) = 0 coulomb

The voltage source is no longer zero, however. In fact it is getting stronger as time goes by according to the formula:

  • E(t) = 20t volts

Remember that the initial conditions cannot be used directly as given! Just like before, the second one needs to be changed into an initial condition involving I'(0) by using the relationship:

I'(0) = (E(0) - R I(0) - q(0)/C) / L

that we derived earlier.

Use sol3 as the solution variable this time, plot on the interval 0 ≤ t ≤ 5, and make the plot blue.

Go to Mathematica now and get to work!

Let's go see what you should have gotten...


Compass If you're lost, impatient, want an overview of this laboratory assignment, or maybe even all three, you can click on the compass button on the left to go to the table of contents for this laboratory assignment.
 
 

ODE Laboratories: A Sabbatical Project by Christopher A. Barker

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