Calculating Node Voltage using Nodal Analysis

In summary, the circuit is driven by a voltage source Vs(t)= 8.2 cos(1.8 t − 0.25 )V and has the elements G1= 5 S, G2= 7.6 S, G3=3.8 S, L1= 20 H, and C1= 5×10−2 F. The task is to find the node voltage of Node 1, V1, by selecting Node 4 as the reference node and using KCL and KVL. The components directly connected between nodes 1 and 4 are the voltage source, and this information can be used to determine the potential difference between the two nodes.
  • #1
TheBigDig
65
2
1. Homework Statement
The circuit is driven by a voltage source,
Vs(t)= 8.2 cos(1.8 t − 0.25 )V .

The circuit elements are given as follows.
G1= 5 S,G2= 7.6 S,G3=3.8 S
(Gi is the conductance of corresponding resistor Ri)
L1= 20 H,C1= 5×10−2 F

If we select Node 4 as the reference node, find the node voltage of Node 1, V1.

2. Relevant equations
Σ Ik = 0

ΣVk = 0

3. The attempt at a solution
I've been able to find values for the resistance R1 = 0.2Ω , R2 = 0.132Ω and R3 = 0.263Ω but continuing on from their is a bit of a struggle. I'm unsure as to how I can apply KCL and KVL in a way that will enable me to find the voltage.

AC-steady-b.jpg


 
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  • #2
Hi TheBigDig,

Please retain the formatting template headings when you construct your homework help request posts. This time I've re-inserted them for you and fixed the excessive use of bold font.

Regarding the problem, what component is directly connected between nodes 1 and 4?
 
  • #3
gneill said:
Hi TheBigDig,

Please retain the formatting template headings when you construct your homework help request posts. This time I've re-inserted them for you and fixed the excessive use of bold font.

Regarding the problem, what component is directly connected between nodes 1 and 4?
The voltage source?
 
  • #4
TheBigDig said:
The voltage source?
Yes. What can you conclude from that regarding the potential difference between nodes 1 and 4?
 
  • #5
TheBigDig said:
If we select Node 4 as the reference node, find the node voltage of Node 1, V1.

Are you sure that's what the question asks?
 

1. How do you determine the reference node when using nodal analysis?

The reference node is typically chosen to be the node with the most connections or the node with the most unknown current or voltage values. It is usually denoted by the symbol "0".

2. What is the difference between supernode and supermesh in nodal analysis?

A supernode is created when two or more essential nodes are connected by a voltage source. In this case, the supernode is treated as a single node and the voltage across the voltage source is considered as a known value. A supermesh, on the other hand, is created when two or more essential branches are connected by a current source. In this case, the supermesh is treated as a single loop and the current through the current source is considered as a known value.

3. How do you handle dependent voltage sources in nodal analysis?

Dependent voltage sources are treated as unknown variables in nodal analysis and are represented by a variable, such as "Vx". The value of the voltage source can then be calculated using Ohm's Law or Kirchhoff's Voltage Law once the nodal analysis equations are set up.

4. What are the limitations of nodal analysis?

Nodal analysis assumes that all elements in the circuit are linear, which means their current-voltage relationship follows Ohm's Law. It also assumes that all connections between elements are ideal and have no resistance. Additionally, nodal analysis can become complex and time-consuming for circuits with a large number of nodes.

5. Can nodal analysis be used for circuits with AC sources?

Yes, nodal analysis can be used for circuits with AC sources. However, the nodal analysis equations must be modified to consider the frequency and phase of the AC sources. It is also important to note that capacitors and inductors must be taken into account in the nodal analysis equations for AC circuits.

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