# Electric circuits I

#### Course Information:

Catalog Description:

This course presents the fundamentals of circuit analysis. It begins with basic concepts such as voltage, current, sources and Ohm’s law; Kirchhoff’s current and voltage laws. then it proceeds to develop general and powerful procedures (nodal and mesh analyses) used in analyzing electric circuits. These methods are first applied to resistive circuits and later to circuits with more complex elements such as capacitors and inductors. Circuits with DC sources as well as those with sinusoidal sources are analyzed.

Also, we will study Superposition, source transformation, and maximum power transfer theorems, Thevenin’s and Norton’s theorems.

Course Objectives:

The topics of this course are part of fundamental theory of electrical engineering and provide depth in analysis, design, and implementation skills in those areas of electrical engineering needed to solve problems in the domain of electrical engineering.

Course Learning Outcomes (CLO):

At the end of this course, the students are expected to be able to define concepts of electric current, voltage, power, Kirchhoff’s current and voltage laws. Use Ohm’s Law in series and parallel connections. Use Thevenin’s theorem and Maximum power transfer and superposition theorems for circuit analysis.

The students can apply nodal and mesh analysis to solve DC circuits. Apply superposition and source transformation methods to solve DC circuits. And will be familiar with inductors and capacitors properties.

The students can also solve series/parallel Linear DC and AC circuits. And be familiar with essential EE instruments such as Digital Multimeters. And using some simulation software to analyze electric circuit.

Some Lows and Equation:

Ohm’s law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points, and inversely proportional to the resistance between them.

where is the potential difference measured across the resistance in units of volts; is the current through the resistance in units of amperes and is the resistance of the conductor in units of ohms.

Kirchhoff’s Current Law or KCL, states that the “total current or charge entering a junction or node is exactly equal to the charge leaving the node as it has no other place to go except to leave, as no charge is lost within the node “. In other words, the algebraic sum of ALL the currents entering and leaving a node must be equal to zero, I(exiting) + I(entering) = 0. This idea by Kirchhoff is commonly known as the Conservation of Charge.

Kirchhoff’s Voltage Law or KVL, states that “in any closed loop network, the total voltage around the loop is equal to the sum of all the voltage drops within the same loop” which is also equal to zero. In other words, the algebraic sum of all voltages within the loop must be equal to zero. This idea by Kirchhoff is known as the Conservation of Energy.

Nodal Analysis:

The aim of nodal analysis is to determine the voltage at each node relative to the reference node (or ground).

Mesh Analysis:

The Mesh Current Method, also known as the Loop Current Method, is quite similar to the Branch Current method in that it uses simultaneous equations, Kirchhoff’s Voltage Law, and Ohm’s Law to determine unknown currents in a network. It differs from the Branch Current method in that it does not use Kirchhoff’s Current Law, and it is usually able to solve a circuit with less unknown variables and less simultaneous equations, which is especially nice if you’re forced to solve without a calculator.

# Thevenin’s and Norton Theorem:

Thevenin’s theorem states that any circuit composed of linear elements can be simplified to a single voltage source and a single series resistance (or series impedance for AC analysis). Norton’s theorem is the same except that the voltage source and series resistance are replaced by a current source and parallel resistance. Furthermore, it is easy to convert a Thevenin equivalent to a Norton equivalent and vice versa.

Thevenin and Norton equivalent circuits are fundamental approaches to analyzing both AC and DC circuits. It is important to understand the steps involved in converting a circuit to its Thevenin or Norton equivalent, but more important still is understanding how these techniques can help you to analyze and design actual electronic devices.

Maximum power transfer:

Maximum power transfer theorem states that the DC voltage source will deliver maximum power to the variable load resistor only when the load resistance is equal to the source resistance.

Similarly, Maximum power transfer theorem states that the AC voltage source will deliver maximum power to the variable complex load only when the load impedance is equal to the complex conjugate of source impedance.

So, we have a maximum power when .

### Superposition Theorem:

The superposition theorem states that in any linear bilateral network that consisting of two or more independent sources, current through (or voltage across) an element is the algebraic sum of the currents through (voltages across) that element caused by each independent source acting alone with all other sources are replaced by their internal resistances. We know that as long as the linearity exists between the source and contribution, the total contribution due to various sources acting simultaneously is equal to the algebraic sum of individual contributions due to individual source acting at a time.

1. electric circuit symbol and formula:

Summary:In this course we introduced basic concepts such as current, voltage, and power in an electric circuit. To actually determine the values of these variables in a given circuit requires that we understand some fundamental laws that govern electric circuits. These laws, known as Ohm’s law and Kirchhoff’s laws, form the foundation upon which electric circuit analysis is built.

we discuss some techniques commonly applied in circuit design and analysis. These techniques include combining resistors in series or parallel, voltage division, current division.

After we Having understood the fundamental laws of circuit theory (Ohm’s law and Kirchhoff’s laws), we are prepared to apply these laws to develop two powerful techniques for circuit analysis: nodal analysis,

which is based on a systematic application of Kirchhoff’s current law(KCL), and mesh analysis, which is based on a systematic application of Kirchhoff’s voltage law (KVL). With the two techniques to be developed in, we can analyze any linear circuit by obtaining a set of simultaneous equations that are then solved to obtain the required values of current or voltage.

Also, to handle the complexity in some electric circuit, Thevenin’s and Norton’s theorems allow us to simplify and isolate a portion of network while the remaining portion of the network is replaced by an equivalent network. Finally, we discuss the concepts of superposition, source transformation, and maximum power transfer.

formation, and maximum power transfer.