# Nodal Analysis eBook

content

• Introduction
• Reference Node
• Node Voltages
• Nodal Analysis Steps
• Complicated Cases

• Circuits with Non-grounded Voltage Sources
• Circuits with Dependent Current Sources
• Circuits with Dependent Voltage Sources

• More Problems

# Nodal Analysis Steps

1) Identify all nodes in the circuit. Call the number of nodes N.

2) Select a reference node. Label it with reference (ground) symbol. As a general rule, the reference node is usually chosen to be

# Nodal Analysis - Circuit with Dependent Voltage Source

Determine the power of each source after solving the circuit by the nodal analysis.

Answers: $P_{I_x}=0.497W, P_{1A}=-1.806W, P_{2A}=4.254W, P_{3V}=-3.87W,$ and $P_{5V}=-3.552W$

Solution

I. Identify all nodes in the circuit.
The circuit has 6 nodes as highlighted below.

# Nodal Analysis – 6-Node Circuit

Determine the power of each source after solving the circuit by the nodal analysis.

Solution
I. Identify all nodes in the circuit.
The circuit has 6 nodes as indicated below.

# Nodal Analysis - Dependent Voltage Source

Use nodal analysis method to solve the circuit and find the power of the $3\Omega$ - resistor.

Solution

I. Identify all nodes in the circuit.
The circuit has 3 nodes as shown below.

# Nodal Analysis - Dependent Current Source

Deploy nodal analysis method to solve the circuit and find the power of the dependent source.

Solution
I. Identify all nodes in the circuit. Call the number of nodes $N$ .
The circuit has 4 nodes:

Therefore, $N=4$ .

# Nodal Analysis - Dependent Voltage Source (5-Nodes)

Solve the circuit with the nodal analysis and determine $I_x$ .

Solution
1) Identify all nodes in the circuit. Call the number of nodes $N$ .
There are five nodes in the circuit:

# Nodal Analysis - Supernode

Solve the circuit with nodal analysis and find $I_x$ and $V_y$ .

Solution
1) Identify all nodes in the circuit. Call the number of nodes $N$ .
There are four nodes in the circuit:

# Nodal Analysis Problem with Dependent Voltage and Current Sources

Solve the circuit with the nodal analysis and determine $i_x$ and $V_y$ .

Solution
1) Identify all nodes in the circuit. Call the number of nodes $N$ .
The circuit has 5 nodes. Therefore, $N=5$ .
Solve the circuit by nodal analysis and find the power of $Is_1$ .