Why RC Circuits Require Differential Equations

Looks at a case of a capacitor discharging while connected to a resistor. Loop rules are used to arrive at a differential equation (where the rate of change of a variable is related to the variable itself). Some discussion then of the importance and use of differential equations as well as what to expect when we solve them.

[@oberoiddroidus2114]

Good point, showing slope lines. Did not find that in the videos of Van Biezen, Jason Haffner nor Gilbert Strang.

[@MiguelELJr]

Awesome content! Thanks for sharing

[@CGKAYA-qe9dc]

Because they re function of time.

[@willthecat3861]

AFAIK, the loop equation is wrong. It should be Vc-Vr = 0

[@lbccphysics]

Something of a Physicist/Engineering disagreement of where minus signs go. If V_R = -RI then it's V_C + V_R. If V_R = +RI then absolutely you're correct.

[@lbccphysics]

What's important is that the differential equation gets us a negative exponential as the solution instead of a positive one. A lot of ways you can define things so that it works that way.

[@frederickwilt5541]

Or you just use a calculator/program that knows how to do RC computations.