MESH ANALYSIS

A mesh is a loop that does not contain other loop within it. It applies KVL to find the unknown currents and only applicable to a circuit that is a planar.

• Planar Circuit- is one that can be drawn in a with no branches crossing one another.

• Non Planar Circuit- can be handled using nodal analysis, but they will not be considered in this text.

Steps to determine mesh currents:

1. Assign mesh currents to the n meshes
2. Apply KVL to each of the n meshes. Use ohm's law to express the voltages in terms of the mesh currents.
3. Solve the resulting n simultaneous equations to get the mesh currents.

Mesh Analysis with Current Sources 

• Case 1: When a current source exists only in one mesh. Set the mesh current is equal to the the current source.

• Case 2: When a current source is exists between two meshes it will form a Super Mesh. Super mesh, created by excluding the current.

Properties of a Super Mesh:

1. Current source in the super mesh provides the constraint equation necessary to solve for the mesh currents.
2. A super mesh has no current of its own,
3. A super mesh requires the application of KVL and KCL.

NODAL ANALYSIS

Nodal Analysis with Voltage source

Two Cases to consider:

• Case 1: A voltage source is connected between a non-reference node and a reference node. The voltage of a non-reference is equal to the voltage source.

• Case 2: A voltage source is connected between two non-reference node will form the Super Node. Super node is formed by enclosing voltage source connected between two non-reference nodes and any elements connected in a parallel with it.

Properties of a Super Node:

1. The voltage source inside the super node provides a constant equation needed to solve for the node voltages.
2. It has no voltage of it's own.
3. It requires the application of both KCL and KVL. 

BASIC LAWS

These basic laws, known as Ohm's law and Kirchhoff's law, form the foundation upon which electric circuit analysis is built.

Ohm's Law
  Ohm's law states that  the voltage v across a resistor is directly proportional to the current i flowing through the resistor.

  The resistance R of an element denotes the ability to resist the flow of electric current; it is measured in ohms. It is represented by this equation

v = iR

Nodes, Branches and Loops 

Branch represents a single element such as a voltage source or a resistor.

Node is the point of connection between two or more branches.

Loop is any closed path in a circuit.

In this figure, an example of branches, node, and loop in an electrical circuit is shown.

Kirchhoff's Law

  There are two parts of Kirchhoff's law, the Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL).

• Kirchhoff's Current Law states that the algebraic sum currents entering a node is zero. In alternative form, the sum of current entering a node is equal to the sum of the current leaving the node.
• Kirchhoff's Voltage Law states that the algebraic sum of all voltages around a close path is zero.

The sum of voltage drop = The sum of the voltage rises.



Situations often arise in circuit analysis when the resistors are neither in  parallel nor in series. It can be simplified using three-terminal equivalent networks. These are the WYE or TEE  and DELTA and PI network, they can occur by themselves or as part of a large network.

In this figure, we can identify a Wye network if it is forming a letter Y and Tee if the form of the network is a letter T.

In identifying Delta network is when the form of the network is a triangle. In PI network by simply identifying it in pi form.

Delta to Wye Conversion

Wye to Delta Conversion

R_a = R₁R₂ + R₂R₃ + R₃R₁/ R₁

R_b = R₁R₂ + R₂R₃ + R₃R₁/ R₂

R_c = R₁R₂ + R₂R₃ + R₃R₁/ R₃





BASIC CONCEPTS

Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C).

Current is the time rate of change of charge, measured in Amperes (A).

• Direct Current (dc) is a current that remains constant with time.
• Alternating Current (ac) is a current that varies sinusoidally with time.

Two common types of current: Alternating Current (AC) and Direct Current (DC).

 

Voltage or Potential Difference is the energy required to move a unit charge through an element , measured in volts (V). 

Power is the time rate of expending or absorbing energy, measured in watts (W).

Circuit Elements is simply an interconnection of the elements.  

• Active element is capable of generating energy.
• Passive element absorbs energy.
• Voltage and current resources

Sources

• Ideal independent source is an active element that provides a specified voltage or current that is completely independent of another circuit elements.
• Ideal dependent source is an active element in which source quantity is controlled by another voltage or current. 

 

Introduction

An electric circuit is an interconnection of electrical elements.

In this figure, a simple electric circuit is shown. It consists of three basic elements: a battery, a lamp and connecting wires. Such a simple circuit can exists by itself; it has several applications, such as a flashlight, a search light and so forth.