# Mesh Analysis - (4 meshes)

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In summary, the conversation discusses Mesh Analysis and its application to a circuit with four meshes. The four meshes are identified and described using a Cartesian coordinate system. The loop currents are also discussed, with an emphasis on their direction. The correct setup for the supermesh equation is provided, correcting previous errors. The current in the branch between meshes 2 and 3, which was assumed to be equal to I_0, is actually a combination of the two loop currents, I_3 and I_2.

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Mesh Analysis -- (4 meshes)

## Homework Statement

http://img185.imageshack.us/img185/1541/screenshot01ly9.jpg [Broken]

V=IR
KVL

## The Attempt at a Solution

Loop 1 is the top left loop.
Loop 2 is the top right loop.
Loop 3 is the bottom right loop.
Loop 4 is the bottom left loop.
(Think of the quadrants in the cartesian coordinate system... that's my loop and loop currents).

Loop currents are going in the CW direction.

For Loop 1:

-14 + I_1 + (I_1 - I_2) + (I_1 - I_4) = 0

For Loop 2:

I_2 = 2mA

For Loop 3 & 4:

Since they are super meshes because of the shared current source... this is what I have:

4mA = I_3 - I_4
-- and --
using the supermesh idea, and short-circuiting the shared 4mA current source...

I4 + 2*I3 + I3 + I4 = 0... which is 3I_3 + 2I_4 = 0

Is my setup correct?

If so, this is what I did...

solved for I_4 in the equation 3I_3 + 2I_4 = 0... I_4 = (-3I_3) / 2

I plugged that I_4 into the eq. 4mA = I_3 - I_4... and I got I_3 = 2mA.

I assumed I_0, what we're trying to find, is equal to I_3. Is this a valid assumption since the current is going around that mesh?

Last edited by a moderator:
Your supermesh equation is incorrect. Starting from the lower left it should be 1k*i_4 + 1k*(i_4 - i_1) + 2k*(i_3 - i_2) + 1k*i_3 = 0

Because of that, your assumption about I_0 is also wrong. The current in that branch is flowing between meshes 2 and 3, so the current is a combination of the two: I_0 = I_3 - I_2.

Yes, your setup and solution seem correct. Assuming that I_0 is equal to I_3 is a valid assumption because the current is indeed going around that mesh. Great job using the supermesh concept to simplify the problem! Keep up the good work.

## 1. What is Mesh Analysis and why is it important in circuit analysis?

Mesh Analysis is a method used to analyze circuits by considering the current flow in each individual mesh or loop. It is important because it allows us to determine the currents and voltages in a circuit, which are crucial in understanding the behavior of electronic systems.

## 2. How many meshes are typically used in Mesh Analysis?

In general, there can be as many meshes as there are independent loops in a circuit. However, in most practical cases, there are usually 2-4 meshes in a circuit.

## 3. Can Mesh Analysis be used for both DC and AC circuits?

Yes, Mesh Analysis can be used for both DC and AC circuits. However, in AC circuits, we must consider the impedance of the components in addition to the resistances in the mesh equations.

## 4. What are the basic steps to perform Mesh Analysis?

The basic steps for Mesh Analysis are:

1. Identify the meshes in the circuit.
2. Assign a current variable for each mesh and write down the loop equations using Kirchoff's Voltage Law (KVL).
3. Solve the resulting equations simultaneously to find the mesh currents.
4. Use the mesh currents to determine the voltages and currents in the rest of the circuit.

## 5. Are there any limitations to Mesh Analysis?

Yes, there are a few limitations to Mesh Analysis:

• It can only be used for circuits with a closed loop.
• It cannot be used for circuits with dependent sources.
• If there are more than 4 meshes in a circuit, it can become complicated and time-consuming to solve.