Transient Response: Analyzing Current with Thevenin's & Mesh/Nodal Analysis

[pforpashya]

Homework Statement

http://s741.photobucket.com/user/pforpashya/media/studybitch/untitled_zps4cac3f38.png.html?filters[user]=137200878&filters[recent]=1&sort=1&o=0

Homework Equations

The Attempt at a Solution

Well I already got the solution and also verified answer in simulation.

My question is, while solving for t>0 current through capacitor I obtained using Thevenins eq.
while writing equation for vth i have to consider vc(0)=3v with the open circuited vth while applying mesh analysis.

Now if i try to do with nodal analysis and if i apply kcl at middle node do i have to consider the v(0)=3v in series with capacitor if no then please tell me why?

 

[gneill]

Homework Statement

http://s741.photobucket.com/user/pforpashya/media/studybitch/untitled_zps4cac3f38.png.html?filters[user]=137200878&filters[recent]=1&sort=1&o=0

Homework Equations

The Attempt at a Solution

Well I already got the solution and also verified answer in simulation.

My question is, while solving for t>0 current through capacitor I obtained using Thevenins eq.
while writing equation for vth i have to consider vc(0)=3v with the open circuited vth while applying mesh analysis.

Now if i try to do with nodal analysis and if i apply kcl at middle node do i have to consider the v(0)=3v in series with capacitor if no then please tell me why?

Hi pforpashya. Welcome to Physics Forums.

I'm not sure that I understand your question accurately. I believe that you wish to know when and why to include the initial capacitor voltage in the analysis, is that correct?

For the first step in your analysis you determined the potential on the capacitor at time t = 0 (just before the switch K is closed). That becomes the initial potential on the capacitor for the next steps in the analysis. Since you're only looking to find the capacitor current you don't really care where the initial capacitor voltage ends up in the modelling process.

If you choose to use a Thevenin equivalent model for the analysis, then you can either treat the capacitor and its initial voltage as the load that is separated from the circuit when you build the model, or you can take the uncharged capacitor as the load and leave its initial voltage with the rest of the circuit when you create the Thevenin model. So the choices are:

In the top circuit, the initial capacitor voltage V_o remains with the load and the Thevenin voltage V_th depends only on the 5V source in your circuit. In the bottom circuit, V_o has been folded into the Thevenin model, so V'_th depends upon both the 5V source and V_o.

Does that help you?

 

[pforpashya]

Thnks for your reply.

i have to verify answer with Nodal analysis. When I am applying nodal analysis in the middle node what will be the equation of current flowing through capacitor?


if i consider node to be v1 then current through capacitor is 0.5 d/dt(v1-3)? or 0.5d/dt (V1)?...the battery present due to initial condition, is it becoming redundant when i apply kcl?

In same way is it true for inductor, that current initially flowing through inductor not considered when applying kvl to that loop,just it is utilize to calculate k?
thanks in advance

 

[gneill]

Thnks for ur reply.

i have to verify answer with Nodal analysis. When I am applying nodal analysis in the middle node what will be the equation of current flowing through capacitor?


if i consider node to be v1 then current through capacitor is 0.5 d/dt(v1-3)? or 0.5d/dt (V1)?...the battery present due to initial condition, is it becoming redundant when i apply kcl?

In same way is it true for inductor, that current initially flowing through inductor not considered when applying kvl to that loop,just it is utilize to calculate k?
thnx in advance

For transient response, the initial conditions should be included in the analysis. For capacitors and inductors these take the form of voltage sources and/or current sources.

 

[rezeew]

When using nodal analysis, you do not need to consider the initial voltage across the capacitor (v(0)=3v) because it is not connected to the middle node. Nodal analysis is used to analyze the current flowing into and out of a particular node, and since the capacitor is not connected to the middle node, its initial voltage does not affect the current at that node. However, when using Thevenin's equivalent circuit, you do need to consider the initial voltage across the capacitor because it is part of the equivalent circuit and affects the overall voltage and current in the circuit.