Differential Equations R-L Circuit

Say this prayer: it helps!

St. Michael the Archangel defend us in battle. Be our protection against the wickedness and snares of the Devil. May God rebuke him, we humbly pray, and do thou most Heavenly host, by the power of God cast into hell Satan and all the evil spirits who roam around the world seeking the ruin of souls. Amen.

Here we shall use the fact that the equation is separable to get to the solution.

First notice in the diagram that we have gotten rid of the capacitor. Thus, we eliminate it from our original equation as well. The equation we get is thus L dI/dt + RI = E.

Next we have the separating process with and expression in front of dI and an expression in front of dt.

Next in the process is integrating over the variables, dI on the left and dt on the right. After checking the appropriate integral table and doing a little algebra ....

.... we then solve for I noting that there are two parts of the equation, a steady state part(a constant), and a transient part (that dies out over time) as shown.

Back to the previous section.

Back to RLC circuits ... RLC circuits

Back to the Hanging Chain ... Hanging Chain

Go back to Gauss' Law Problem from here!

1st Gauss' Law Example problem ... Gauss Law Example 1.

Navigate below to go back to the start!

You can go to DE Ex2 here...D.E. Ex2.

You can go to DE Ex1 here ...D.E. Ex1.

Or

Back to the Hanging Chain ... Hanging Chain

Go back to Gauss' Law Problem from here!

1st Gauss' Law Example problem ... Gauss Law Example 1.

Navigate below to go back to the start!

You can go to DE Ex2 here...D.E. Ex2.

You can go to DE Ex1 here ...D.E. Ex1.