I was trying to do this practice problem, but the constants of the equation are killing me!
The question is:
-The differential equation for the voltage vc across the capacitor is dvc/dt=(V(t)-vc)/RC.
Find the formula for the general solution of the RC circuit equation above if the voltage source is contant for all time, i.e. V(t)=K for all t.
-Find the solution for the voltage vc(t) with initial-value vc(0)=1 in the RC circuit with constant voltage source V(t)=K
The first question I get stuck because once I replace V(t)=K, it becomes dvc/dt=(K-vc)/RC, now I could isolate RC by dvc/dt=1/RC(K-vc). The problem is after that I'm having problems differentiating.
The second question is easy. Once the formula for the general solution of the RC circuit is found all I have to do is plug it in vc(t)=1 and solve for contant right?