Nodal Analysis - Dependent Current Source


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.

II. Select a reference node. Label it with reference (ground)
symbol.

All nodes have the same number of elements. We prefer to select one of the nodes connected to the voltage source to avoid having to use a supernode.
the reference node

III. Assign a variable for each node whose voltage is unknown.
We label the remaining three nodes as shown above.

IV. If there are dependent sources in the circuit, write down equations that express their values in terms of other node voltages.
There is one dependent source, which is a current controlled current source. We need to write  -2I_1 in terms of node voltages.  I_1 is the current passing through the  2\Omega - resistor. Applying the Ohm's law,
 I_1 = \frac{V_2-V_3}{2\Omega}.
Hence,  -2I_1 = V_3-V_2.

V. Write down a KCL equation for each node.
Node  V_1:  \frac{V_1}{3 \Omega}+\frac{V_1-V_2}{1\Omega}-2I_1=0.
 \to 4V_1-6V_2+3V_3=0 (Eq. 1).

Node  V_2:  2I_1+\frac{V_2-V_1}{1\Omega}-2A+\frac{V_2-V_3}{2\Omega}=0.
Please note that we avoid using all unknowns except node voltages. Using  I_1 in this KCL equation introduces an unnecessary unknown to the equations set. Substituting  2I_1 = V_2-V_3 and rearranging results in:
 -2V_1+5V_2-3V_3=4 (Eq. 2).

Node  V_3 has a voltage source connected to. Therefore,  V_3=10V. Substituting this in Eq. 1 and Eq.2 leads to
 \left\{\begin{array}{l} 4V_1-6V_2=-30 \\ -2V_1+5V_2=34 \end{array}\right..
By solving the system of equations,
 V_1=6.75V and  V_2=9.5.

Now, we need to find the voltage across the dependent current source and the current passing through it. Lets start with  I_1.
 I_1 = \frac{V_2-V_3}{2\Omega}=-0.25 A.

Assuming positive terminal placed on the node of  V_1, the voltage across the dependent current source is  V_1-V_2=-2.75V. The current flowing through the dependent current source is  -2I_1=0.5A. Therefore the power of the dependent current source is  -2.75 \times 0.5 = -1.375W . Because the current direction and the voltage polarity is in accordance with the passive sign convention and the power is negative, the dependent current source is supplying power.

5 thoughts on “Nodal Analysis - Dependent Current Source

  1. Thanks, but correct me if i'm wrong but all nodes doesn't have the same number of elements:

    *Node 4 has 3 elements = 2 ohms, 3 ohms and 10V

    *Node 2 has 4 elements = -2I1 dependet source, 2A current source, 1 ohms and 2 ohms.

    *Node 3 has 4 elements = 2 ohms, 10V, 2A current source and 2 ohms.

    *Node 1 has 3 elements = 1 ohms, 3 ohms and -2I1 dependet source.

    Why choose node 4 with 3 elements as reference node if node 2 and node 3 have 4 elements or the most number of elements?

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