[SOLVED] Nodal Analysis for AC Circuit

Can anyone help me in solving this circuit by using nodal analysis

Do you truely require help for such elementary school level task ?
This is also very true for the followings.
https://www.edaboard.com/threads/203897/
https://www.edaboard.com/threads/200478/

I1=-polar(5, 90)=-j*5, I2=polar(10, 0)=10
R1=3, G1=1/R1, R2=6, G2=1/R2, Y12=1/(j*3)+1/(-j*5)=-j*(2/15)

G1*V1+Y12*(V1-V2)=(G1+Y12)*V1-Y12*V2=I1
G2*V2+Y12*(V2-V1)=-Y12*V1+(G2+Y12)*V2=I2

step 1: label all nodes, already done they are v1, v2 or GND.

step 2: make an assumption about the direction of current flowing in each node, doesn't need to be correct, just consistent. (draw arrows on each path (not node) which way you guess the current is flowing)

step 3: express the current sources as complex numbers, i.e. encode the phase into the value

step 4: write 0 = the sum currents flowing in (+ve) and out (-ve) of nodes with respect to the voltage difference, impedance and current direction of each node (BE CONSISTENT).

i.e. current flowing from V1 to V2 would be (v1 - v2) / -5j

step 5: doing step 4 repeatedly should form X equations with X unknowns which can be solved simultaneously

ALWAYS BE CONSISTENT WITH CURRENT DIRECTION, SIGN (+ve or -ve) AND WHICH SIDE OF THE EXPRESSION YOU WRITE THE TERMS ON! SERIOUSLY YOU CAN NOT GET THIS QUESTION CORRECT IF YOU DON'T

pancho_hideboo said:

Wrong.
It has to be "Y12*(V1-V2), Y12=-j*(2/15)".

Click to expand...

That was just an example man to demonstrate that the current flowing between the nodes is the difference of there electrical potential divided by impedance 'Z', or multiplied by conductance 'Y'. Y = 1/Z

But yes the true impedance between those sources is the parallel complex sum of the impedance of both the inductor and the capacitor. :smile:

allsey87 said:

That was just an example man to demonstrate that the current flowing between the nodes is the difference of there electrical potential divided by impedance 'Z', or multiplied by conductance 'Y'. Y = 1/Z

Click to expand...

See my appends. I showed complete nodal equation sets for this circuits.
In nodal equation, Y12 has to be "Y12=-j*(2/15)".
[Note]Sign of this "Y12" is different from "Y12" of Y-parameters.

Your "(v1 - v2) / -5j" could cause misunderstanding to starter of this thread since you mention like following.

allsey87 said:

i.e. current flowing from V1 to V2 would be (v1 - v2) / -5j

Click to expand...