S domain analysis problem, just need a little help

[Derill03]

Okay i need to find expressions for v1 and v2 and I am using nodal analysis:

these are not the final the equations just initial equations by first look


I am good finding expression for v1,
(2/s)-(v1/1)-((v1-v2)/(2/s)) = 0

Where i am stuck is with the current source and 2 ohm res. in series

For v2,
((v1-v2)/(2/s))-(v2/2s)-(v2/2)-(5/s) = 0 this is my derivation that I am unsure of

the reason i think this is wrong for v2 is in my head i see instead of v2/2 - 5/s i see something like ((v2-v)/2)-(5/s)? where v is voltage between current source and res

Can anyone help me understand where I am right or wrong thanks

**BTW see attachment for circuit**

 

[gneill]

For nodal analysis you're only concerned with summing the currents. The 2Ω resistor in series with the 5u(t) current source is not going to alter that current that it pulls from the V2 node. So ignore the resistor!

FYI, your entries for the capacitor impedance look a bit off. 1/(s*200 mF) should yield something like 5/s.

 

[Derill03]

so would v2 be:

((v1-v2)/(5/s)) - v2/2s - 5/s?

my mistake on the cap transformation it is 5/s which is equal to 1/0.2s my bad

 

[gneill]

so would v2 be:

((v1-v2)/(5/s)) - v2/2s - 5/s?

my mistake on the cap transformation it is 5/s which is equal to 1/0.2s my bad

That looks fine

 

[DeeNos]

Based on the nodal analysis equations provided, it seems like you are trying to solve for the voltages v1 and v2 in a circuit with a current source and a 2 ohm resistor in series. It is important to note that nodal analysis is a method used to solve for unknown voltages in a circuit, not currents. Therefore, your equations for v1 and v2 should only include voltage terms, not current terms.

In your equation for v1, it looks like you are using the current division rule to solve for the current through the 2 ohm resistor. However, this is not necessary since you are already using nodal analysis to solve for the voltage across the 2 ohm resistor.

For v2, it is correct to use the current source and 2 ohm resistor in series, as shown in your equation. However, the voltage term v2/2 should be multiplied by the conductance (1/2) instead of the impedance (2) since it is in series with a current source. Additionally, the voltage term (v2-v)/2 should be multiplied by the impedance (2) since it is in parallel with the current source.

I would recommend redrawing the circuit and double-checking your equations to ensure that all voltage terms are correctly represented. Remember to also consider the direction of the current through each element when writing your nodal equations. I hope this helps and good luck with your analysis!