**CIRCUIT ANALYSIS**

**MESH ANALYSIS**

**NODAL ANALYSIS**

Mesh analysis

is a method that is used

to solve planar circuits for the currents

(and indirectly the voltages) at any place in the circuit. Planar circuits are circuits that can be drawn on a plane surface with no wires crossing each other.

Mesh analysis works by arbitrarily assigning mesh currents in the essential meshes.

An essential mesh is a loop in the circuit

that does not contain any other loop.

Assign mesh currents

i1, i2, .., in to the n meshes. Current direction need to be same in all meshes either clockwise or anticlockwise.

Apply KVL to each of the n meshes.

Use Ohm’s law to express the voltages in terms of the mesh currents.

Solve

the resulting n simultaneous equations to get the mesh currents

EXAMPLE

A circuit with two meshes..

Apply

KVL

for each mesh..

Mesh 1 :

Mesh 2 :

Solve

for the mesh currents..

*Use

i

for the

mesh current

and

I

for a

branch current

In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents.

Nodal analysis is possible when all the circuit elements branch constitutive relations have an admittance representation.

Kirchhoff’s current law

is used to develop the method referred to as nodal analysis

Step to determines nodal :

Note all

connected wire segments in the circuit. These are the nodes of nodal analysis.

Select one node as the ground reference

. The choice does not affect the result and is just a matter of convention. Choosing the node with most connections can simplify the analysis.

Assign a variable for each node

whose voltage is unknown. If the voltage is already known, it is not necessary to assign a variable.

For each unknown voltage,

form an equation based on Kirchhoff's current law.

Basically, add together all currents leaving from the node and mark the sum equal to zero.

If there are voltage sources between two unknown voltages,

join the two nodes as a super node.

The currents of the two nodes are combined in a single equation, and a new equation for the voltages is formed.

Solve the system of simultaneous equations

for each unknown voltage.

Steps to Determine Mesh Currents:

REFERENCE NODE

The reference node is called the

ground node

where V = 0

EXAMPLE

V1

,

V2,

and

V3

are unknowns for which we solve using

KCL

Current And Node Voltage

KCL at Node 1

KCL at Node 2

KCL at Node 3

prepared by :

erna,myra,dayang