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, $N=4$.

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.

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.

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## Join the Conversation

1. khans sahil says:

Thank you sir

2. Ram Kaushik says:

thanks a lot !! im passing my test coz of u .... cheers mate 🙂 🙂

3. Juan dela Cruz says:

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?

4. Chetan Jadhav says:

Thanks a Lot! It really helped me, made my concepts clear and solved many doubts. Thank you.

5. it's more than a lecture's hall. thanks for this a mazing website

6. Aakash Yadav says:

The Best Teacher