Mesh Analysis Part (1/2) – 5 Steps Mesh Analysis with illustration & example – DC Circuit Analysis

Hey there! In this video, I will be discussing Mesh Analysis, a method used for analyzing circuits in electrical engineering. Mesh Analysis is a powerful tool that can help us understand how current flows through a circuit and determine important parameters such as voltage and power.

Before we dive into the details of Mesh Analysis, let me first explain what a mesh is in the context of electrical circuits. A mesh is a loop in the circuit that does not contain any other loops within it. In other words, a mesh is a closed path through which current can flow without encountering any other loops.

Now, let’s move on to the steps involved in Mesh Analysis. There are five steps in total, and I will be walking you through each of them with the help of illustrations and examples to make it easier to understand.

Step 1: Assign Mesh Currents

The first step in Mesh Analysis is to assign mesh currents to each of the meshes in the circuit. Mesh currents are the currents that flow through each of the meshes and are represented by variables such as I1, I2, I3, and so on. By assigning mesh currents, we can create equations that describe the relationships between the currents and the voltages in the circuit.

Let’s take a look at an example to understand this better. Consider the circuit shown below:

In this circuit, we have three meshes labeled as I1, I2, and I3. By assigning mesh currents to each of these meshes, we can write equations that describe the relationships between the currents and the voltages in the circuit.

For example, we can write the following equations based on the circuit shown above:

1. V1 = I1 * R1 + (I1 – I2) * R2

2. V2 = (I2 – I1) * R2 + (I2 – I3) * R3

3. V3 = I3 * R3

These equations describe the relationships between the voltages V1, V2, and V3 and the mesh currents I1, I2, and I3 in the circuit. By solving these equations simultaneously, we can determine the values of the mesh currents and the voltages in the circuit.

Step 2: Define Mesh Current Loop Equations

The next step in Mesh Analysis is to define mesh current loop equations for each of the meshes in the circuit. Mesh current loop equations are equations that describe the relationships between the mesh currents and the voltages in the circuit.

To define mesh current loop equations, we use Kirchhoff’s Voltage Law (KVL), which states that the sum of the voltages around any closed loop in a circuit is equal to zero. By applying KVL to each mesh in the circuit, we can write equations that relate the mesh currents to the voltages in the circuit.

Let’s go back to the example circuit we discussed earlier. We can define the following mesh current loop equations for each of the meshes in the circuit:

For Mesh 1 (I1):

I1 * R1 + (I1 – I2) * R2 = V1

For Mesh 2 (I2):

(I2 – I1) * R2 + (I2 – I3) * R3 = V2

For Mesh 3 (I3):

I3 * R3 = V3

These equations represent the relationships between the mesh currents and the voltages in the circuit. By solving these equations simultaneously, we can determine the values of the mesh currents and the voltages in the circuit.

Step 3: Solve Mesh Equations Simultaneously

The next step in Mesh Analysis is to solve the mesh equations we defined in the previous step simultaneously to determine the values of the mesh currents and the voltages in the circuit. This can be done using algebraic manipulation and techniques such as substitution and elimination.

Let’s continue with our example circuit to illustrate this step. By solving the mesh current loop equations for each mesh in the circuit simultaneously, we can determine the values of the mesh currents I1, I2, and I3 and the voltages V1, V2, and V3 in the circuit.

After solving the equations, we might find that:

I1 = 2A, I2 = 3A, I3 = 1A

V1 = 10V, V2 = 15V, V3 = 5V

These values represent the currents and voltages in the circuit based on the mesh analysis we performed. By solving the equations simultaneously, we can determine the values of the currents and voltages in the circuit.

Step 4: Calculate Power and Voltage Drops

Once we have determined the values of the mesh currents and the voltages in the circuit, we can calculate important parameters such as power and voltage drops in the circuit. Power is the rate at which energy is transferred in the circuit, while voltage drops represent the decrease in voltage as current flows through the circuit elements.

To calculate power and voltage drops, we use Ohm’s Law, which states that the current flowing through a circuit element is equal to the voltage across the element divided by the resistance of the element. By using Ohm’s Law, we can calculate the power dissipated in each circuit element and the voltage drops across the elements.

Let’s take a look at an example to understand this better. Consider the circuit shown below:

In this circuit, we have determined the values of the mesh currents and the voltages based on our mesh analysis. Now, we can calculate the power dissipated in each circuit element and the voltage drops across the elements using Ohm’s Law.

For example, we can calculate the power dissipated in R1 as:

Power_R1 = I1^2 * R1

We can also calculate the voltage drop across R1 as:

Voltage Drop_R1 = I1 * R1

By calculating the power dissipated in each circuit element and the voltage drops across the elements, we can understand how energy is transferred in the circuit and the impact of current flow on the circuit elements.

Step 5: Verify Results and Check for Errors

The final step in Mesh Analysis is to verify the results we obtained and check for any errors in our analysis. It is important to verify the values of the mesh currents and the voltages in the circuit to ensure that our analysis is correct and accurate.

To verify the results, we can compare the calculated values of the mesh currents and the voltages with the values obtained from other analysis methods such as Nodal Analysis or with experimental measurements. By comparing the results, we can ensure that our analysis is accurate and reliable.

Additionally, we should also check for any errors in our analysis by reviewing our calculations and equations. It is important to double-check our work to ensure that we have not made any mistakes in the calculations or the application of the principles of Mesh Analysis.

By following these five steps in Mesh Analysis, we can analyze complex circuits and determine important parameters such as current, voltage, power, and voltage drops. Mesh Analysis is a powerful tool that can help us understand the behavior of circuits and design efficient electrical systems.

I hope you found this video helpful and informative. Stay tuned for Part 2, where we will delve deeper into Mesh Analysis and explore more advanced concepts and techniques. Thank you for watching!

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