Introduction to Electrical Circuits, Lecture notes of Electrical Circuit Analysis

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Electrical Circuits I

Lecture 1

Basic dc circuit elements, series and parallel Networks Ohm's law and Kirchoff's laws Nodal Analysis Mesh Analysis Source Transformation Method Superposition Theory Thevenin's Theorem and Norton Theorem Maximum Power Transfer Alternating current Fundamentals and AC generation RMS value, average value, form factor and crisp factor Phasor concept Relation between voltage and current in resistor, capacitor and inductor Response of RL and RC circuits Sinusoidal response of RLC circuit Series Resonance

Course Contents

Basic Electrical Quantities

Basic quantities: current, voltage and power.

Electric current:

Electric current in a wire is defined as the net amount of charge that passes through the wire per unit time , and is measured in amperes (A). where i = current in amperes q = charge in coulombs t = time in sec. 1 Ampere = 1 Coulomb per second (C/s) Current in circuits physically realized by movement of electrons. Direction of current must be specified by an arrow.

dt

dq

i 

By convention, current direction defined as flow of positive charge. Note that positive charge is not flowing physically. Electrons have negative charge. They move in the opposite direction of current.

electron motion positive current direction In general, current can be an arbitrary function of time. Constant current is called direct current (DC). Current that can be represented as a sinusoidal function of time (or in some contexts a sum of sinusoids) is called alternating current (AC).

We use polarity (+ and – on batteries) to indicates which direction the charge is being pushed Voltage is the energy required to move a unit charge through an element, measured in volts (V)

dq

d

v



where v = voltage in volts ω = energy in Joules q = charge in coulombs

v

A B

i

Circuit Element

Voltage ~ Pressure Electric Current ~ Water Current Sponge ~ Resistance

Elements of electrical circuits

Active elements

Active elements are the elements that can generate energy or power, such as voltage and current sources. Ideally, a voltage source produces Vs volts regardless of the current absorbed or produced by the connected device.  Ideally, a current source produces Is amps regardless of the current in the connected device. In a particular circuit, there can be active elements that absorb power – for example, a battery being charged.

Passive elements

passive elements are the elements that can not generate energy, such as resistors, capacitors and inductors. The ability of a material to resist (impede, obstruct) the flow charge is called its resistivity. It is represented by the letter R. A resistor is a circuit element that dissipates electrical energy (usually as heat) Real-world devices that are modeled by resistors: incandescent light bulbs, heating elements, long wires Resistance is measured in Ohms (Ω) Resistor is indicated by the symbol

resistors

Ohm’s Law

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. The mathematical equation that describes this relationship is: R v i  where v is the potential difference measured across the resistance in units of volts; i is the current through the resistance in units of amperes and R is the resistance of the conductor in units of ohms.

Two elements are in series if the current that flows through one must also flow through the other. R 1 R 2 Series  If we wish to replace the two series resistors with a single equivalent resistor whose voltage-current relationship is the same, the equivalent resistor has a value given by

Req  R 1  R 2

Consider two resistors in series with a voltage v across them: v 1 v 2 1 2 1 1 R R R v v   1 2 2 2 R R R v v  

R 1

R 2

v i Voltage division:

Resistors in Parallel

When the terminals of two or more circuit elements are connected to the same two nodes, the circuit elements are said to be in parallel.  If we wish to replace the two parallel resistors with a single equivalent resistor whose voltage-current relationship is the same, the equivalent resistor has a value given by 1 2 1 2 R R R R R (^) eq  