# Category Archives: Resistive Circuits

Solved problems in resistive circuits such as nodal analysis, mesh analysis, superposition, source transformation, Thevenin and Norton theorems and so on

# Superposition Method - Circuit With Dependent Sources

Determine $I_x$, $I_y$ and $V_z$ using the superposition method.

Solution
I. Contribution of the $-2V$ voltage source:
We need to turn off the current source by replacing it with an open circuit. Recall that we do not turn off dependent sources. The resulting circuit is shown below.

# Superposition Problem with Four Voltage and Current Sources

Determine $V_x$ and $I_x$ using the superposition method.

Solution
I. Contribution of the $-5V$ voltage source:

To find the contribution of the $-5V$ voltage source, other three sources should be turned off. The $3V$ voltage source should be replaced by short circuit. The current source should be replaced with open circuits, as shown below.

# 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, $N=5$.

# Problem 1-16: Voltage Divider

Find $V_x$ (or $v_x(t)$) and $I_x$ (or $i_x$) using voltage division rule.
a)

b)

c)

d)

Solution

a)

Voltage divider: $V_x=\frac{5\Omega}{2\Omega+5\Omega}\times 14 V=10 V$
Ohm's law: $I_x=\frac{V_x}{5 \Omega}=2 A$