Nodal Analysis

Case 1: If the source voltage is connected to the

non-reference node and reference node(ground).

Consider this is a circuit:

Find V2?

 To solve for the circuit given:

• Analyze the problem.
• Assume node 1 for V1 and node 2 for V2.
• You can see to the given circuit that the 12 voltage source is connected to the reference and non-reference node, therefore the value for V1 is 12 v.
• Equation for V2:

• V2(1/j2 + 1/3 + 1/j4) - V1/j2 = 0

                               V2(0.33 - j0.75) - 12/j2 = 0
                                V2 = j6/(0.33 - j0.75)
                                 V2 = -6.70 + 2.949 V or 7.3225 /_156.25 V

Case 2: If the source voltage is not connected

to the reference node(ground) it is a SUPERNODE.

Consider this is a circuit:

To solve for the given circuit:

• Analyze the circuit.
• Assume V1 for the first node and V2 for the second node.
• You can see to the circuit that the source voltage is not connected to the reference node.
• Therefore, it is a SUPERNODE.
• When solving SUPERNODE, you must kill the source voltage and change it to short. See circuit below!

• Using KCL, you can get the equation value for the SUPERNODE.
• Supernode equation: 
• Using KCL:
• i1 + i2 + i3 = 0   ====> the sum of current entering the node is equal to the sum of current leaving the node.

• Get the value for i1, i2, and i3.
• Using Ohm's Law:
• i1 = V1/j1
• i2 = V2/3
• i3 = V2//j2

•  Substitute the equation for i1, i2, and i3.
• Final equation:
•  (V1/j1) + (V2/3) + (V2/j2) = 0 ====> equation 1

• Then  for the second equation, the circuit must back to original form. See circuit below!

• You can now use KVL to get the second equation.
• Using KVL:
• V1 + 12 - V2 = 0     ====> From Higher to Lower potential . :))
• V1 - V2 = -12          ====> equation 2

• Substitute equation 1 to equation 2 to find the value of the unknown.
• Finish!