## What is Mesh Analysis?

Mesh analysis is defined as

*The method in which the current flowing through a planar circuit is calculated.*

A planar circuit is defined as the circuits that are drawn on the plane surface in which there are no wires crossing each other. Therefore, a mesh analysis can also be known as loop analysis or mesh-current method.

### What is Branch?

A branch is defined as the path that connects two nodes such that it contains a circuit element. If the branch belongs to only one mesh, then the branch current and the mesh current will be equal to each other.

## Procedure of Mesh Analysis

The following steps are to be followed while solving the given electrical network using mesh analysis:

**Step 1:**

To identify the meshes and label these mesh currents in either clockwise or counterclockwise direction.

**Step 2:**

To observe the amount of current that flows through each element in terms of mesh current.

**Step 3:**

Writing the mesh equations to all meshes using Kirchhoffâ€™s voltage law and then Ohmâ€™s law.

**Step 4:**

The mesh currents are obtained by following Step 3 in which the mesh equations are solved.

Hence, for a given electrical circuit the current flowing through any element and the voltage across any element can be determined using the node voltages.

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### Mesh Current Diagram

The below diagram is a circuit with mesh currents labelled as I_{1}, I_{2}, and I_{3} and the arrows represent the direction of the mesh current.

## What is Super Mesh Analysis?

Super mesh analysis is used for solving huge and complex circuits in which two meshes share a common component as a source of current.

## Example of Mesh Analysis

**Example 1:**

In the given circuit 90v is the battery value, 5A is the current source and the three resistors are 9 ohms, 6 ohms, and 8 ohms. Using mesh analysis, determine the current across each resistor and potential difference.

**Solution: **

Letâ€™s first determine the ground as shown in the figure

Let the potential be V_{A}, V_{B}, and V_{C} as shown in the figure

Let I_{1} and I_{2} be the currents flowing through the two loops in the clockwise direction as shown in the figure

Therefore,

+V_{B} – V_{1} – V_{2} = 0

90 – I_{1}R_{1} – R_{2}(I_{1} – I_{2}) = 0

90 – 9I_{1} – 6(I_{1} – I_{2}) = 0

-15I_{1} + 6I_{2} = -90

5I_{1} – 2I_{2} = 30 (this is obtained by dividing the equation with -3)

Substituting I_{2} as -5 since the direction of I_{2} is opposite to the actual direction of current

Therefore,

I_{1} = 4A

So, through R_{1}, 4A current is flowing and through R_{3}, 5A current is flowing.

Now the potential difference at V_{A} = 90V

At V_{B}, the potential difference is V_{2} = I_{2} – R_{2}

Therefore, V_{B} = 54V

At V_{C}, the potential difference is V_{3} = I_{3} – R_{3}

V_{C} – 54 = 40

V_{C} = 94V

Stay tuned with BYJUâ€™S to learn more about other concepts of Physics.

## Frequently Asked Questions â€“ FAQs

### What is the difference between loop and mesh?

The difference between loop and mesh is that a loop is a closed path in a circuit in which none of the nodes repeat more than once. While a mesh is a closed path in a circuit in which no other paths are present.

### What are the limitations of mesh analysis?

The following are the disadvantages of mesh analysis:

- Mesh analysis is useful only when the circuit is planar.
- As the number of meshes increases, the number of equations increases, which makes it inconvenient for solving.

### Which Kirchhoffâ€™s law is used in mesh analysis?

Kirchhoffâ€™s voltage law is used in mesh analysis.

### What is the difference between mesh and nodal analysis?

The difference between mesh and nodal analysis is that nodal analysis is an application of Kirchhoffâ€™s current law, which is used for calculating the voltages at each node in an equation. While mesh analysis is an application of Kirchhoffâ€™s voltage law which is used for calculating the current.

### What is a dependent source?

A dependent source in an electrical network is defined as either a voltage source or a current source whose value is dependent on the voltage or current in the network. Voltage-controlled voltage source, voltage-controlled current source, current-controlled current source, and current-controlled voltage source are the classification of the dependent sources.