Lecture 2: Voltage and Current Source, Active and Passive Components PDF

INTRODUCTION TO ELECTRICAL AND ELECTRONICS ENGINEERING LECTURE NO: 2 VOLTAGE SOURCE AND CURRENT SOURCE, ACTIVE AND PASSIVE COMPONENTS Ideal Voltage Source  An independent voltage source is that the value of the voltage is not dependent on either the magnitude...

INTRODUCTION TO ELECTRICAL AND ELECTRONICS ENGINEERING LECTURE NO: 2 VOLTAGE SOURCE AND CURRENT SOURCE, ACTIVE AND PASSIVE COMPONENTS Ideal Voltage Source  An independent voltage source is that the value of the voltage is not dependent on either the magnitude or direction of the current flowing through the source.  That is, an ideal voltage source is a two-terminal device that maintains a fixed voltage drop across its terminals.  Model representation: Voltage-Current characteristics of an ideal constant voltage source  An ideal voltage source has zero internal resistance.  Independent current source  An ideal independent current source is a two-terminal device that supplies a specified current to the current in which it is placed independently of the value and direction of the voltage appearing across its terminals.  Model representation:  Voltage-Current Characteristics of an ideal Current source  The internal resistance of an ideal current source is infinite.  Active Components and Passive Components  Active Components: Those devices or components which required external source to their operation is called Active Components.  Examples: Transistor, Operational amplifier etc..  Passive Components:  Those devices or components which do not required external source to their operation is called Passive Components.  Examples: Resistor, Capacitor, Inductor etc…  Resistor  The circuit element used to model the current-resisting behaviour of a material is the resistor.  Georg Simon Ohm, a German physicist, is credited with finding the relationship between current and voltage for a resistor.  This relationship is known as Ohm’s law.  Ohm’s law states that the current I flowing in a circuit is directly proportional to the applied voltage V and inversely proportional to the resistance R, provided the temperature remains constant. i-v characteristic of resistor Problem The current flowing through a resistor is 0.8 A when a p.d. of 20 V is applied. Determine the value of the resistance. Resistance  The property of an electric circuit opposing the flow of current and at the time causes electrical energy to be converted to heat is called resistance.  A conductor having high number of free electrons offer less resistance to the flow of current.  The resistance is denoted by the symbol ‘R’ and is measured in Ohm symbolically represented as Ω. Factors affecting the Resistance a) Length of the material (l) b) Cross-sectional area (a) c) Type and nature of the material [If material is conductor, its resistance is less while if it is insulator, its resistance is very high ] d) Temperature  The effect of nature of material is considered through the constant of proportionality denoted by ‘ρ’ (rho) called resistivity or specific resistance of the material.  Where, l = Length in meters  a = Cross sectional area in square meters  ρ = resistivity in ohm-meters  R = Resistance in ohms  A material with highest value of resistivity is the best insulator while the poorest value of resistivity is the best conductor.  The reciprocal of resistance is called conductance (G) and is measured in siemens (S) or mho.  The Reciprocal of resistivity is known as conductivity denoted as σ (sigma).  It is measured in siemens/m. A material having highest value of conductivity is the best conductor while having poorest conductivity is the best insulator.  In the circuit shown in figure, calculate the current i, the conductance G, and the power p.  Solution: Problem  Determine the resistance of 1200 m of copper cable having a diameter of 12 mm if the resistivity of copper is 1.7x10-8 Ωm.  Electrical Power and Energy  When a direct current of I amperes is flowing in an electric circuit and the voltage across the circuit is V volts, then Power in watts, P = V I  Although the unit of energy is the joule, when dealing with large amounts of energy, the unit used is the kilowatt hour (kWh). Ans: Problem  A 100 W electric light bulb is connected to a 250 V supply. Determine (a) the current flowing in the bulb, and (b) the resistance of the bulb. Problem  You have two types of lamps: an LED lamp and a CFL lamp. Both lamps are rated to provide the same level of brightness, but they have different power ratings. The LED lamp has a power rating of 10 watts (W). The CFL lamp has a power rating of 15 watts (W).  You use each lamp for 5 hours per day. Calculate the energy consumed by each lamp in one day and one month (assuming 30 days in a month). Additionally, compare the energy cost if the electricity rate is 6 rupees per kilowatt-hour (kWh). Open Circuit and Short Circuit  Since the value of R can range from zero to infinity, it is important that we consider the two extreme possible values of R.  An element with R = 0 is called a short circuit. For a short circuit, v = i R = 0 showing that the voltage is zero but the current could be anything.  An element with R = infinity is known as an open circuit. For an open circuit, v i = lim = 0 R → R indicating that the current is zero though the voltage could be anything. Capacitor  A capacitor is a passive element designed to store energy in its electric field.  A capacitor consists of two conducting plates separated by an insulator (or dielectric). The capacitance is given by the equation  When a voltage source v is connected to the capacitor, the source deposits a positive charge q on one plate and a negative charge - q on the other.  The capacitor is said to store the electric charge.  The amount of charge stored, represented by q, is directly proportional to the applied voltage v so that, where C, the constant of proportionality, is known as the capacitance of the capacitor.  The unit of capacitance is the farad (F).  i-v characteristic of capacitor  (since q = C v) -------- (1) For a capacitor to carry current, its voltage must vary with time. Hence, for constant voltage, i = 0.  The voltage-current relation of the capacitor can be obtained by integrating both sides of Eq. (1) where v(t0) = q(t0)/C is the voltage across the capacitor at time t0.  Power delivered to the capacitor,  Energy stored in the capacitor, or [ since v = q /C ] Problem Calculate the charge stored on a 3-pF capacitor with 20 V across it. Also find the energy stored in the capacitor. Solution: Problem  A 5μF capacitor is charged so that the pd between its plates is 800 V. Calculate how long the capacitor can provide an average discharge current of 2 mA. Inductor  An inductor is a passive element designed to store energy in its magnetic field.  An inductor consists of a coil of conducting wire. µ = Permeability of the core material  If current is allowed to pass through an inductor, it is found that the voltage across the inductor is directly proportional to the time rate of change of the current.  where L is the constant of proportionality called the inductance of the inductor.  The unit of inductance is the Henry (H).  For an inductor to have voltage across its terminals, its current must vary with time.  Hence, v = 0 for constant current through the inductor. i-v characteristic of inductor  The power delivered to the inductor is  Energy stored in the inductor is  Problem : Find the current through a 5-H inductor if the voltage across it is Solution Problem  The energy stored in the magnetic field of an inductor is 80 J when the current flowing in the inductor is 2 A. Calculate the inductance of the coil.