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, $N=5$ .

Reference Node and Node Voltages

Reference Node
In circuits, we usually label a node as the reference node also called ground and define the other node voltages with respect to this point. The reference node has a potential of $0 V$ by definition. The following symbol is used to indicate the reference node:

The Reference Node Symbol

As mentioned, the selection of the reference node is arbitrary. However, a wise selection can make the solving easier. As a general rule, it is usually chosen to be