Calculating Node Voltage using Nodal Analysis

[TheBigDig]

1. Homework Statement
The circuit is driven by a voltage source,
V_s(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 I_k = 0

ΣV_k = 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.

 

[gneill]

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?

 

[TheBigDig]

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?

 

[gneill]

The voltage source?

Yes. What can you conclude from that regarding the potential difference between nodes 1 and 4?

 

[CWatters]

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?