# Current and static electricity

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<ul><li> 1. 5 Current and Static ElectricityUNIT 1 CURRENT AND STATIC ELECTRICITY Structure 1.1 Introduction Objectives 1.2 DC Circuit and Steady Current and Voltage 1.3 Basic Definitions Related to Circuit Analysis 1.4 Ohms Law and its Limitations 1.5 Resistance 1.5.1 Classification of Substances 1.5.2 Resistance Law 1.5.3 Effect of Temperature on Resistance 1.5.4 Temperature Coefficient of Resistance 1.5.5 Resistance in Series 1.5.6 Resistance in Parallel 1.5.7 Classification of Resistors 1.6 Kirchhoffs Laws 1.6.1 Kirchhoffs Voltage Law 1.6.2 Kirchhoffs Current Law 1.6.3 Application of Kirchhoffs Laws 1.7 Source Transformations 1.8 Heating Effect of Electric Current 1.9 Summary 1.10 Answers to SAQs 1.1 INTRODUCTION The development of electricity and its application has a great history. In 600 BC, Thales, a Greek Mathematician, philosopher could produce a feel of electricity. He found that when amber is rubbed against wool or fur it gets electrified and attracts small particles of straw and produces spark. Static positive and negative charges can be created by rubbing amber with a piece of wool or fur. Some of the valence electrons from the one material become free electrons and are transferred to another material. The charges on the amber and the wool tend to remain stationary, thus the name static electricity. The names like electricity, electrons and electronics originated from the word elektron which is the Greek word of amber. Above was the first experiment in the field of static electricity. After a long time in 1785, Coulomb, in France, first established the mathematical relation for such experiment. He defined the charge and force between two charges. In 1800, Galvani and Volta produced the electricity by chemical means. They made the first DC source known as battery. In 1825-26, Ohm established the relation between voltage and current which became the basis for Kirchhoffs Voltage and Current law in 1845. Most of the useful application of static electricity do not rely on static discharge which ionize the air and occurs when the electric force field between a positive charge and a negative charge becomes too strong. Rather they make use of the force of attraction between unlike charges or the force of repulsion between like charges. These forces are used to move charged particles to desired location. </li></ul><p> 2. 6 In this unit, we will learn basic definitions of the terms which are related to electricity, such as voltage, current, power and energy. Circuit element resistance will be discussed in detail. Electricity The relationship between current (I), voltage (V) and resistance (R) was discovered by a German scientist named Georg Ohm. In this honor this relationship is named Ohms law. Here, in this unit, we will discuss Ohms law with its limitations and two basic laws of the behaviour of current and voltage, which are known as Kirchhoffs Laws. These laws enable scientists to understand and, therefore, evaluate the behaviour of electrical networks. How to convert a voltage source into a current source and vice-versa will also be discussed under source transformation technique. Objectives After studying this unit, you should be able to explain the concept of DC circuit and steady voltage, current, power and energy, define Ohms law and its limitations, explain the resistance law and its dependency on temperature, find the equivalent resistance for parallel and series circuits, write the voltage and current equations using Kirchhoffs voltage and current laws, understand source transformation technique, and calculate the power loss and energy dissipated in electric circuit. 1.2 DC CIRCUIT AND STEADY CURRENT AND VOLTAGE Figure 1.1 shows a simple DC circuit which consists of DC source and passive element like resistance. Different types of DC sources are cell, battery, DC generator etc. In DC Analysis voltage and current remain constant with respect to time, while alternating current (or AC voltage) changes direction and magnitude with respect to time. Voltage and current waveforms for given simple DC circuit are shown in Figures 1.2(a) and (b). RV I Figure 1.1 : Simple DC Circuit V 0 t I 0 t V R (a) (b) Figure 1.2 : Waveforms (a) Direct Voltage; and (b) Direct Current 3. 7 Current and Static Electricity1.3 BASIC DEFINITIONS RELATED TO CIRCUIT ANALYSIS In general, we will use uppercase letters V, I, P to indicate constant voltage, current and power respectively and lower case letters v, i, p to indicate instantaneous values of time varying signals. Let us know about some basic definition such as voltage, current, power and energy which are commonly used in electrical. Voltage (or Potential) Voltage is the electric pressure that causes current to flow. Voltage is also known as electromotive force (e.m.f.), or potential difference. All these terms refer to the same thing, that is, the force that sets charges in motion. Potential difference is actually a potential energy difference that exists between two points. An electric charge possesses potential energy (energy at rest). Potential energy is capable of doing work when we provide the right conditions to convert it from its stored form into another form (potential to kinetic energy). Voltage is the work done for moving unit positive charge from one point to another in electric field. Energy ( ) Voltage ( ) Charge ( ) W V Q = Potential difference can also be defined as the work done for bringing a unit positive charge from infinity to any point in electric field. Instantaneous value of voltage can be given as joules/coulombor volts. dw v dq = Current Electric current is the moment of charged particles in a specified direction. The charged particle is often referred to as a current carrier. In a solid, such as copper wire the charged particle (current carrier) is the electron. However, in both liquids and gases, the ions are free to move about and become current carriers. In semiconductors, the charge is carried by electron and holes, the holes behaving like positive charges. In conducting materials, a large number of free electrons are available which move from one atom to other at random when a potential difference is applied between two points of the conducting material and the current starts flowing. In electricity the amount of current is specified in terms of the charge and time required to move the charge past a given point. The amount of electric current is, therefore, specified in Coulombs per second (ampere). When we think about current, keep two points in mind. First, the effect of current is almost instantaneous. Current in a wire travels at nearly the speed of light, i.e. 186,000 miles per second (3 108 meters per second). Second an individual electron moves much more slowly. It may take minutes for an electron to travel a few feet in the wire. The rate of flow of charges through any cross-section of conductor is called a current and is denoted as i. Amperes dq i dt = where i is the instantaneous value of the current (value at any particular instant). 4. 8 Hence one ampere is the current, which flows when a charge of one coulomb moves across the cross-section of a conductor in one second. Electricity The steady current I is given as Amperes Q I t = where Q is the uniform flow of the charges through the cross-section of the conductor in time t. Otherwise CoulombsQ i dt= The term static electricity comes into the picture when flow of electron is steady or the flow of electron is at constant drift velocity. Static electricity includes the study of current, potential and power related to DC circuits. Electrical Power Power is defined as the rate of doing work and it is expressed in Joules per second Joules/second W P t = When one coulomb of electrical charge moves through a potential difference of one volt in one second the work done is one Joule/sec and in electrical engineering it is expressed as Watt. So, power supplied WattsP V I= By Ohms law ( ) WattsP I R I= 2 WattsI R= or, 2 Watts V V P V R R = = For AC circuit or circuits with unidirectional source, electrical power is expressed as WaP v i tt= 2 i R= where, p, v, i all stands for instantaneous values. Energy Electrical energy is the total amount of work done and it is expressed in Joules or in Watt-Second in electrical engineering. In DC circuit, energy is dissipated in the form of heat in resistor for a time t seconds and is given by Watt-sec.W P t= V I t= 2 Watt-sec.W I Rt= or 2 Watt-sec. V W t R = For AC circuits, energy can be expressed as 5. 9 Current and Static Electricity c.Watt-seW pd t= Watt-sec.W v id t= where, p, v, i are instantaneous values. Energy expressed in terms of Kilo-Watt-hour (kWh) or units, sine Watt-sec. is a small unit, 1 unit of energy = 1 kWh Electrical energy supplied to the consumer is charged by Power Distribution Companies in terms of Standard Energy Units known as Kilo-Watt-Hours. 1.4 OHMS LAW AND ITS LIMITATIONS Ohms law is a central concept to most electrical engineering theories. In 1825-26, Ohm gave the relation between electric current and potential. This relation is known as Ohms law. According to Ohms law potential difference across a conductor is directly proportional to the current flowing through the conductor, the temperature of the conductor remains constant. i.e. V I V RI= where R is the constant of proportionality is known as resistance, V R I = (resistance in ohms) Electrical resistance is the hindrance to the flow of electrons in a given material. V and I represent constant value of current and voltage. Above relation is shown in the form of resistance curve in Figure 1.3, which is linear in nature. (a) Resistance Curve for Ohms Law (b) Circuit Represents Ohms Law Figure 1.3 Ohms law can also be applied to AC circuits volv Ri= ts where v and i are instantaneous values of voltage and current respectively. Limitations of Ohms Law (a) Ohms law is valid only if the physical conditions like temperature, pressure remain constant. 6. 10 (b) Ohms law is not applicable to non-metallic conductors. For example, for silicon carbide, the relationship is given by , where k and n are constants. This relation is not linear. n V k I= Electricity (c) Since the resistance also depends on the length and area of cross section of conductor, so for the application of Ohms law the dimensions of conductor should remain constant. Example 1.1 A lamp load of 1000 resistance is connected across the DC supply of 25 V. What is power absorbed in lamp and what amount of heat will be released in 10 sec. Solution The current taken by the lamp load 25 0.025 Amp 100 I = = 25 m Amp= Power loss 2 I R= 2 (0.025) 1000= 3 625 10 Watts = 625 mW= Heat released or energy consumed in 10 sec. 2 W I Rt= Pt= 3 625 10 10 = 2 625 10 = 6.25 joules= . SAQ 1 An electric iron operates from a 230 volt outlet and draws 8 amperes of current. At Rs. 4/ kWh, how much does it cost to operate the iron for 2 hours? 1.5 RESISTANCE It is the property of any substance due to which it opposes the flow of current through it. It has the same role in electric circuit as that of friction in mechanical system. This opposition is basically due to the molecular structure of the substance. When electrons flow through any substance then they collide with the other molecules or atoms of the substance. In each collision, some energy is dissipated in the form of heat. So we can say due to resistance some energy is wasted in the form of heat (which is given by I2 Rt). The resistance is defined as the ratio of voltage and current in any circuit and its unit is ohm (). ohm ( ) V R I = 7. 11 Current and Static Electricity Reciprocal of resistance is known as the conductance (G) and its unit is mho (). 1 mho I G R V = = . 1.5.1 Classification of Substances On the basis of their resistance, substances may be classified as good conductor, semiconductor and bad conductor. Good Conductor Materials with low resistance and high conductance are known as the good conductors of electricity. Example Metals (like copper, aluminum, silver etc.), acids and electrolytes. Semiconductor Materials which are bad conductors at low temperature and good conductors at high temperature are classified as the semiconductors. Such materials are partially conducting, but also has properties of an insulator. The amount of current conduction that can be supported can be varied by doping the material with appropriate materials, which results in the increased presence of free electrons for current flow. They have medium resistance (between good and bad conductors) at room temperature. Example Germanium, Silicon, GaAs. Bad Conductors Materials which offer very high resistance to flow of electricity are known as the bad conductors of electricity. They are normally used as the insulator in electrical machines. Example Mica, Glass, Paper, Rubber, Wood, Bakelite etc. 1.5.2 Resistance Law Resistance of any material is directly proportional to the length of material and inversely proportional to its area of cross-section. i.e. R l 1 R A l R A or l R A = where l = length in metre, A = area of cross section in metre2 , and resistivity of material (specific resistance).= It is defined as the resistance between the opposite faces of a metre cube of any material. A R l = 2 metre = ohm metre = Ohm-metre 8. 12 Reciprocal of resistivity is known as conductivity or the specific conductance. It is denoted by and its unit is /metre. Electricity 1 = . mho/metr l G A = e 1.5.3 Effect of Temperature on Resistance In ideal conditions, resistance is the constant element of the circuit. But as the current flows, heat is produced, and temperature is increased. With increase in temperature following effects are observed : (a) Resistance of the metal conductors increases with increase in temperature. The Resistance-temperature graph is a straight line and shown in Figure 1.4. Figure 1.4 : Resistance-Temperature Curve for Metals (b) Resistance of alloy also increases with increase in temperature. But this increment is relatively slow and irregular. (c) Resistance of semiconductors decreases with increase in temperature. At very low temperature, they acts like insulators but at high temperature they show the property of conductors. (d) Resistance of electrolytes and insulators (bad conductors) decreases with increase in temperature. 1.5.4 Temperature Coefficient of Resistance Let R0 is resistance at any initial temperature t0 and Rt is the resistance at higher temperature t. Then increment in resistance (Rt R0) is directly proportional to initial value of resistance R0 and increment in temperature (t t0). i.e. 0 0 0 0( )tR R R t t = where 0 is the temperature coefficient of resistance referred to temperature t0 0 0 0 0( ) tR R R t t = If initial temperature t0 = 0o C then 0 0 tR R R t = . Unit of temperature coefficient is per o C. Resistance at any temperature is defined as 0 (1 )tR R t= + (here t0 = 0o C) 9. 13 Current and Stat...</p>

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