Differential Equation Approach to solving First Order Circuits

[RadiationX]

We are doing transient circuit analysis in one of my engineering courses.
There are two ways of solving these types of circuits:

1. The step by step approach

2. The differential equation approach.

The step by step method is well documented in our textbook, but the differential equation approach is not.

Does anyone know of a website that describes how to use the differential equation approach for solving first order transient circuits?

 

[chaoseverlasting]

Dunno the website, but you use Kirchoff's laws (Potential drop across a loop =0) to form a linear DE which you solve.

 

[DefaultName]

Dunno the website, but you use Kirchoff's laws (Potential drop across a loop =0) to form a linear DE which you solve.

For the differential approach, use KVL and KCL. Write down the device rules (i(t) = C dv(t)/dt), etc... combine them by solving for the appropriate variables.

 

[euler_fan]

I am curious, is the step by step approach the Laplace transform method, if not, is there any reason you could not use said method. I prefer to use the Laplace transform myself.

 

[chaoseverlasting]

Err... I don't know the Laplace transform approach, just the DE one. Its pretty simple. You just write out the equations for KVL and KCL, and then write current as dq/dt or emf as L di/dt to get a Linear DE and solve that.