# Mesh analysis(3)

Hey there, welcome back to another video on mesh analysis! Today, we will be diving deeper into the topic of mesh analysis and exploring more complex circuits. So grab your pen and paper, and let’s get started!

Mesh analysis is a powerful technique used in circuit analysis to solve for unknown currents in a circuit. It is based on Kirchhoff’s voltage law and involves creating loops in the circuit to analyze the current flow. In our previous videos, we covered the basics of mesh analysis and how to apply it to simple circuits. In this video, we will be tackling more challenging circuits with multiple loops and sources.

Before we begin solving complex circuits, let’s do a quick recap of the key concepts of mesh analysis. In mesh analysis, we first identify the meshes in the circuit. A mesh is a closed loop in the circuit that does not contain any other loops. Each mesh will have a current flowing through it, which we will need to solve for. We assign a direction for each mesh current and apply Kirchhoff’s voltage law to set up equations for each mesh.

Now, let’s move on to solving a circuit with multiple meshes. Consider the following circuit:

In this circuit, we have three meshes labeled as I1, I2, and I3. To apply mesh analysis, we need to create equations for each mesh based on Kirchhoff’s voltage law. Let’s start with mesh I1:

Loop equation for mesh I1:

V1 – R1*I1 – R3*(I1 – I2) – R4*(I1 – I3) = 0

Next, let’s move on to mesh I2:

Loop equation for mesh I2:

-R3*(I2 – I1) – R2*I2 – R5*(I2 – I3) = 0

Lastly, we have mesh I3:

Loop equation for mesh I3:

-R4*(I3 – I1) – R5*(I3 – I2) – R6*I3 = 0

Now that we have set up the equations for each mesh, we can solve for the unknown currents by solving the system of equations. This may involve some algebraic manipulation and substitution to simplify the equations and find a solution. Once we have solved for the mesh currents, we can use Ohm’s law to find the voltages and currents in the rest of the circuit.

One important thing to note when solving circuits with mesh analysis is to always be mindful of the direction of the mesh currents. A wrong direction assignment can lead to incorrect results and make it harder to solve the circuit. It is also important to label the voltages and resistors in the circuit correctly to avoid confusion while setting up the equations.

Now let’s take a look at a more practical example of a complex circuit that requires mesh analysis to solve:

In this circuit, we have four meshes labeled as I1, I2, I3, and I4. To solve this circuit using mesh analysis, we need to set up four loop equations based on Kirchhoff’s voltage law. I won’t go into the details of deriving each equation, but let’s write out the loop equations for each mesh:

Loop equation for mesh I1:

V1 – R1*I1 – R3*(I1 – I2) – R4*(I1 – I4) = 0

Loop equation for mesh I2:

-R3*(I2 – I1) – R2*I2 – R5*(I2 – I3) = 0

Loop equation for mesh I3:

-R5*(I3 – I2) – R6*I3 – V2 = 0

Loop equation for mesh I4:

-R4*(I4 – I1) – R6*I4 + V2 = 0

By solving this system of equations, we can find the values of the mesh currents I1, I2, I3, and I4. Once we have the mesh currents, we can use Ohm’s law to calculate the voltages and currents in the rest of the circuit.

As you can see, mesh analysis is a powerful tool for solving complex circuits with multiple loops and sources. It allows us to systematically analyze the circuit and find the unknown currents with ease. By practicing and understanding the concepts of mesh analysis, you can tackle even the most challenging circuits with confidence.

That’s all for today’s video on mesh analysis. I hope you found this tutorial helpful in understanding how to apply mesh analysis to more complex circuits. Remember to practice and keep honing your skills in circuit analysis. Thanks for watching, and I’ll see you in the next video!