Combination Circuits

Table of Contents

What are Combination Circuits

Circuit Analysis

Circuit analysis is important to be able to design and verify the behaviour of our electrical circuits. There are many approaches that can be taken when trying to analyze the same circuit. However certain circuits may be easier to solve using certain techniques. The following are some of the techniques:  

Kirchhoff's Voltage Law

The algebraic sum of all voltages around any closed path in a circuit equals zero [3]. This law can be applied to various forms of combination circuits to analyze their behaviour.

Kirchhoff's Current Law

The algebraic sum of all the currents at any node in a circuit equals zero [4]. Similar to KVL, this law can be applied to various forms of combination circuits to analyze their behaviour.

Node Voltage Method

The Node Voltage Method relies on the Kirchhoff’s Current Law and presents an organized method to solve combination circuits. The steps of the method are as follows [2]:

1. 1. Assign a reference node to be ground.
   2. Assign voltages (V­­₁, V₂, etc..) to all other nodes. These are referenced to the reference node.
   3. Write KCL equations for all unknown nodes that are not the reference node. If possible, use Ohm’s Law to relate branch currents to voltages
   4. Solve resulting system of linear equations for unknown node voltages

A comprehensive guide to using this method can be found at this link.

Mesh Current Method

The Mesh Current Method relies on the Kirchhoff’s Voltage Law and Ohm’s Law and an organized method to solve combination circuits. The steps of the method are as follows [5]:

1. 1. Identify the meshes
   2. Assign a current variable to each mesh. Be consistent in the reference current direction chosen for the variables.
   3. Write a KVL equation for each mesh
      1. Voltage sources go in as voltages
      2. Resistor voltages are inputted as R x i_Loop
      3. If two loop currents flow in opposite directions through a resistor, the voltage of said resistor is inputted as R x (i_Loop1- i_Loop2). If the directions are the same, it’s written as R x (i_Loop1+ i_Loop2)
      4. Set the sum of the voltages for each KVL equation equal to zero
   4. Solve the resulting linear KVL equations for all loop currents
   5. Solve for element currents and voltages as needed using Ohm’s Law

A comprehensive guide to using this method can be found at this link.

References

[1] The Physics Classroom, "Combination Circuits." The Physics Classroom [Online]. Available: https://www.physicsclassroom.com/class/circuits/Lesson-4/Combination-Circuits. [Accessed: 15-Jun-2021].

[2] W. McAllister, “Node voltage method” Khan Academy. [Online]. Available: https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-dc-circuit-analysis/a/ee-node-voltage-method. [Accessed: 17-Jun-2021].

[3] Electronics Tutorials, “Kirchhoff’s Voltage Law,” Electronics Tutorials. [Online]. Available: https://www.electronics-tutorials.ws/dccircuits/kirchhoffs-voltage-law.html. [Accessed: 17-Jun-2021].

[4] Electronics Tutorials, “Kirchhoff’s Current Law,” Electronics Tutorials. [Online]. Available: https://www.electronics-tutorials.ws/dccircuits/kirchhoffs-current-law.html. [Accessed: 17-Jun-2021].

[5] W. McAllister, “Mesh current method” Khan Academy. [Online]. Available: https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-dc-circuit-analysis/a/ee-mesh-current-method. [Accessed: 17-Jun-2021].