Nodal Analysis Dependent Current Source 5

Nodal Analysis - Dependent Voltage Source

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Use nodal analysis method to solve the circuit and find the power of the 3\Omega - resistor.
Nodal Analysis Dependent Current Source


Solution

I. Identify all nodes in the circuit.
The circuit has 3 nodes as shown below.
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nodal analysis dependent current source

Nodal Analysis - Dependent Current Source

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

Solution
I. Identify all nodes in the circuit. Call the number of nodes N .
The circuit has 4 nodes:
all nodes
Therefore, N=4 .
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nodal analysis 2-r-t

Nodal Analysis - Dependent Voltage Source (5-Nodes)

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Solve the circuit with the nodal analysis and determine I_x .
Nodal analysis - circuit with dependent voltage source

Solution
1) Identify all nodes in the circuit. Call the number of nodes N .
There are five nodes in the circuit:
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node-voltage-6-i

Reference Node and Node Voltages

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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

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
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Voltage Divider 1-i

Voltage Divider - Voltage Division Rule

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The voltage division rule (voltage divider) is a simple rule which can be used in solving circuits to simplify the solution. Applying the voltage division rule can also solve simple circuits thoroughly. The statement of the rule is simple:

Voltage Division Rule: The voltage is divided between two series resistors in direct proportion to their resistance.


It is easy to prove this. In the following circuit

Voltage Divider

Voltage Divider

the Ohm's law implies that
v_1(t)=R_1 i(t) (I)
v_2(t)=R_2 i(t) (II)
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1-13-c-b-i

Ideal Independent Sources

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1) Ideal Independent Voltage Sources
An ideal independent voltage source is a two-terminal circuit element where the voltage across it
a) is independent of the current through it
b) can be specified independently of any other variable in a circuit.
There are two symbols for ideal independent voltage source in circuit theory:

Symbol for Constant Independent Voltage Source

Symbol for Constant Independent Voltage Source


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