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1.Electric circuit. Electrical charge.

a.electric circuit is as an interconnection of electrical components, each of which we will describe with a mathematical model.

b.The most elementary quantity in an analysis of electric circuits is the electric charge. Our interest in electric charge is centered around its mot ion, since charge in motion results in an energy transfer. Of p<1I1icular interest to us are those s ituations in which the motion is confined

c.to a defin ite closed path An e lec tric c ircuit is essentially a pipe line that facilitates the transfer of c harge from one point to anothe r. The lime rate of c hange of charge constitutes an e lectric current. Mathe matically. the re lationship is expressed as

d.i(l)=dq(t)/dt

e.where i und q represent curre nt and charge, respecti vely (lowercase letters represent time

f.depende ncy, and capital le iters are reserved fo r constant quaJ1lities). The basic unit of current

g.is the ampere (A), and I ampere is I coulomb per second.

2.What is a difference between real and conventional current flow?

The old (conventional) current flow says that where there is a surplus of charge ( meaning positive) the current flows towards a deficient point (which means negative). However later discovery found that electrons which are negatively charged constitute this current flow and electrons move towards a positively charged body - not the other way around. This has now become the electron flow - the movement of electrons from surplus point (negative) towards a less negative (deficient) point. So we can say now that in a complete circuit using for instance a battery, the electron current flows from the Negative side of the battery towards the Positive side via the external load.

Although we know that current flow in metallic conductors results from e lectron motion.the convent ional current flow, which is universally adopted, represents the movement of positive charges. It is important that the reader think of current flow as the movement of positive charge regardless of the physical phenomena that take place. The symbolism that will be used to represent current flow is shown in Fig. J .2. I[ = 2 A in Fig. 1.2a indicates that at any point in the wire shown, 2 C of charge pass from left to right each second. I']. = - 3 A in Fig. 1.2b indicates that at any point in the wire shown, 3 C of charge pass from right to left each second. Therefore, it is important to specify not only the magnitude of the variable representing the current, but also its direction.

3.Why is it important to specify not only the magnitude of the variable representing the current (or voltage), but also its direction?

a.It is important that the reader think of current flow as the movement of positive charge regardless of the physical phenomena that take place. The symbolism that will be used to represent current flow is shown in Fig. J .2. I[ = 2 A in Fig. 1.2a indicates that at any point in the wire shown, 2 C of charge pass from left to right each second. I']. = - 3 A in

Fig. 1.2b indicates that at any point in the wire shown, 3 C of charge pass from right to left each second. Therefore, it is important to specify not only the magnitude of the variable representing the current, but also its direc tion.

4.What are the two types of current? Describe them.

i.The two types of current that we encounter often in our daily lives. alternating current (ac) and direct current (dc), are shown as a function of time in Fig. 1.3.

ii.An electric current that repeatedly changes its direction or strength, usually at a certain frequency or range of frequencies.

iii.DC (direct current) is the unidirectional flow or movement of electric charge carriers (which are usually electrons). The intensity of the current can vary with time, but the general direction of movement stays the same at all times. In a DC circuit, electrons emerge from the negative, or minus, pole and move towards the positive, or plus, pole

5.What is a difference between alternating current and direct current?

 

 

 

 

Alternating

 

Direct Current

 

 

 

 

Current

 

 

 

 

 

 

 

 

 

 

 

 

 

Amount of energy

 

 

Safer to transfer over longer city

 

 

Voltage of DC cannot travel very

 

 

 

 

 

 

 

 

that can be carried:

 

 

distances and can provide more

 

 

far until it begins to lose energy

 

 

 

 

 

power

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Flow of Electrons:

 

Electrons keep

 

Electrons move steadily in one

 

 

 

 

switching directionsforward and

 

direction or 'forward'

 

 

 

 

backward

 

 

 

 

 

 

 

 

 

 

Cause of the

 

 

Rotating magnet along the wire

 

 

Steady magnetism along the wire

 

 

 

 

 

 

 

 

direction of flow of

 

 

 

 

 

 

 

 

electrons:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Frequency:

 

The frequency of alternating

 

The frequency of direct current is

 

 

 

 

currentis 50Hz or 60Hz depending

 

zero.

 

 

 

 

upon the country.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Direction:

 

 

It reverses its direction while

 

 

It flows in one direction in the

 

 

 

 

 

flowing in a circuit

 

 

circuit

 

 

 

 

 

 

 

 

 

 

 

Current:

 

It is the current of magnitude

 

It is the current of constant

 

 

 

 

varying with time

 

magnitude

 

 

 

 

 

 

 

 

 

 

 

 

 

Types:

 

 

Sinusoidal, Trapezoidal,

 

 

Pure and pulsating

 

 

 

 

 

Triangular, Square

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Obtained from:

 

A.C Generator and mains

 

Cell or Battery

 

 

 

 

 

 

 

Passive

 

 

Impedance

 

 

Resistance only

 

 

 

 

 

 

 

 

Parameters:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Power Factor:

 

 

Lies between 0 & 1

 

 

it is always 1

 

 

 

 

 

 

 

 

 

 

Direct current means that the current doesn't change direction. In other words, there is a constant flow

of electrons from minus to plus. It is these electrons that let you recharge a battery, for example. And batteries produce direct current as well.

Alternating current means that the current changes direction, usually tens of times a second. As a result, the electrons don't really move anywhere, they just kind of wiggle back and forth in one place. This still creates electric energy that you can use, for example, to power your lights. Because the current must change direction, it means that the voltage is not constant, but varies sinusoidally between its positive and negative peaks (60V, in the case of your wall outlet).

6.Give the examples of direct current sources.

Flow of electric charge that does not change direction. Direct current is produced by batteries, fuel cells, rectifiers, andgenerators with commutators

some examples of direct current producing sources are batteries, thermocouples, solar cells, and commutator-type electrical machines of the dynamo type.

Batteries already have DC energy stored and ready to use in an electrical appliance. If the power from the battery needed is alternating current, then a dc to ac inverter is required. A thermocouple is a widely used form of temperature sensor and can also be used to convert heat into electrical power. Solar cells convert light directly into electricity by what is called photovoltaic effect. This type of energy is referred to as solar energy. A dynamo, formerly known as an electrical generator, is now better known as a generator that produces direct current. Dynamos were a breakthrough because they were the first electrical generators that could deliver power for industry, and were the cornerstone for the creation of the electric motor, the alternator, and the rotary converter. Because of the dominance and efficiency of alternating current and solid state rectifiers to convert the energy to direct current, dynamos are rarely used today.

Direct current can travel in several ways. It can travel on a conductor, which is generally some form of metallic wire such as copper or aluminum. The wires, or conductors, can also be protected by insulators that resist the flow of electric current, thus allowing multiple currents to travel along different conductors in close proximity. A semi-conductor is kind of a combination of a conductor and an insulator in one. A very wide variety of electronics implement the use of semiconductors. Silicon is a very popular substance used in the making of semiconductors. The current travels by way of electrons or positively-charged "holes" in the electron structure of the silicon. Direct current can also travel through a vacuum as in electron or ion beams. A light bulb is a great example of a simple form of vacuum that electricity travels through.

Direct current is used for a variety of things such as charging batteries and used in almost all electronic devices as the power supply. In some urban areas it is used to propel railways. The production of aluminum uses very large quantities of directcurrent power. Large amounts of power are transmitted via high-voltage direct current from remote generation sites or to interconnect alternating current power grids. Typically the power being transmitted from a power generation site is in alternating current. However, over long distances direct current is more efficient as less power is lost and is transmitted at a lower cost.

A is at a higher potential than point e,

7.What is a voltage? What is an energy?

i.we define the voltage between IWO points in a circuit as the difference in energy level of a unit charge located at each of the two points

ii.

In Fig. l.5a the variable that represents the voltage between points A and 8 has been defined as VI. and it is assumed that point as indicated by the + and - signs associated with the variable and defined in the figure.

The + and – signs define a reference direction for VI' If ~ = 2 Y, then the difference in potential of points A and B is 2 V and point A is at the higher potential. If a unit positive charge is moved from point A through the circuit to point B, it will give up energy to the circuit and have 2 J less energy when it reaches point B. If a unit positive charge is moved from point B to point A. extra energy must be added to the charge by the circuit, and hence the charge will end up with 2 J more energy at poi nt A than it started with at point B.

Work or energy, w(t) or W, is measured in joules (J ); 1 joule is 1 newton meter (N · m).Hence, voltage [v(r) or V] is

measured in volts (V) and I volt is I joule per coulomb; that is, 1 volt = 1 joule per coulomb = 1 newton meter per coulomb. If a unit positive charge is moved between two points, the energy required to move it is the difference in energy level between the two points and is the defined voltage. It is extremely important that the variables used to represent voltage between two points be defined in such a way that the solution will let us interpret which point is at the higher potential with respect to the other.

8.Investigate the voltage-current relationships for energy transfer using the flashlight circuit (battery, switch, light bulb).

a.

b.Let's investigate the voltage-current relationships for energy transfer using the flashlight shown in Fig. 1. 7. The basic elements of a flashlight are a battery, a switch, a light bulb, and connecting wires. Assuming a good battery, we all know that the light bulb will g low when the switch is closed. A current now flows in this closed circuit as charges flow out of the positive terminal of the battery through the switch and light bulb and back into the negative terminal of the battery. The current heats up the filament in the bulb, causing it to glow and emit light. The light bulb converts electrical energy to thermal energy; as a result, charges passing through the bulb lose energy. These charges acquire energy as they pass through the battery as chemical energy is converted to electrical energy. An energy conversion process is occurring in the flashlight as the chemical energy in the battery is converted to electrical energy, which is then converted to thermal energy in the light bulb.

c.

Let's redraw the flashlight as shown in Fig. 1.8. There is a current I fl owing in this diagram. Since we know that the light bulb uses energy, the charges coming out of the bulb have less energy than those entering the light bulb. In other words, the charges expend energy as they move through the bulb. This is indicated by the voltage shown across the bulb. The charges gain energy as they pass through the battery, which is indicated by the voltage across the battery. Note the voltage - current relationships

for the battery and bulb. We know that the bulb is absorbing energy; the current is entering the positive terminal of the voltage. For the battery, the current is leaving the positive terminal, which indicates that energy is being supplied. This is further illustrated in Fig. 1.9 where a circuit element has been extracted from a larger circuit for examination. In Fig. 1.9a, energy is being supplied to the element by whatever is attached to the terminals. Note that 2 A, that is, 2 C of charge are moving from point A to point B through the element each second. Each coulomb loses 3 J of energy as it passes through the element from point A to point B. Therefore, the element is absorbing 6 ] of energy per second. Note that when the element is absorbing energy. a positive current enters the positive terminal. In Fig. 1.9b energy is being supplied by the clement to whatever is connected to terminals A-B. In this case, note that when the element is supplying energy,

a positive current enters the negative terminal and leaves via the positive terminal. In this convention, a negative current in one direction is equivalent to a positive current in the opposite direction, and vice versa. Similarly, a negative voltage in one direction is equivalent to a positive voltage in the opposite direction.

9. Power. What is passive sign convention?

Electric power is the rate at which electric energy is transferred by an electric circuit. The SI unit of power is the watt, one joule persecond.

Passive sign convention

In electronics, which deals with more passive than active devices, electric power consumed in a device is defined to have a positive sign, while power produced by a device is defined to have a negative sign. This is called the passive sign convention.

Resistive circuits

In the case of resistive (Ohmic, or linear) loads, Joule's law can be combined with Ohm's law (V = I·R) to produce alternative expressions for the dissipated power:

where R is the electrical resistance.

10.What is the difference between active and passive circuit elements? Give the examples of typical active and passive elements.

ACTIVE COMPONENTS

The components which produce the energy in the form of current or voltage are called as active components.

Example:transistors etc,. PASSIVE COMPONENTS

The components which stores the energy in the form of current or voltage are called as passive components.

example:inductors,resistors,capacitors etc,.

The three linear passive elements are the Resistor, the Capacitor and the Inductor. Examples of non-linear

passive devices would be diodes, switches and spark gaps. Examples of active devices are Transistors,

Triacs, Varistors, Vacuum Tubes, relays, solenoids and piezo electric devices."

Active Circuit Elements:

Figure 1.1: Active circuit elements

All circuit elements that are capable of supplying electric power to a circuit or to an aspect of the circuit for an indefinitely long time are called Active circuit elements. Batteries and generators are examples of active circuit elements. Figure 1.1 shows circuit symbols used to depict a Voltage Source (an ideal battery) and a Current Source. Notice that the circuit elements show a polarity—either a reference label for the voltage or an arrow giving a reference direction for the current or both. There is also a mathematical equation associated with each circuit element. For a voltage source, V = 5 volts (or any constant) is an example of such an equation. For a current source, I = 2 amperes (or any constant) is another example.

Transistors, vacuum tubes (valves), and many other circuit elements are also active elements even though they cannot supply electrical power to the entire circuit for an indefinitely long time. These components take electrical power from one part of the circuit (often called a power supply) and deliver the power to another part of the circuit (often by way of amplifying a signal) and can do this for an indefinitely long time.

Note that an element is active if it is capable of the above. Even if it is not delivering power to a particular circuit (or an aspect of a particular circuit) it might still be an active circuit element.

Passive Circuit Elements:

Philosophically speaking, any circuit element that is not active is passive. This means that passive circuit

elements Absorb or Dissipate electric power in the long term. In the short term they may store some electric power and then return that power back to the circuit at a later time. Even if a circuit element is 100% efficient in this storage and return process, it is passive because it cannot deliver power over an indefinitely long time. (Of course nothing more than 100% efficient exists. Active circuit elements have a source of energy to draw on, such as the chemicals in a battery. Passive elements do not.) A resistor is a good example of a passive circuit element. The following picture shows circuit symbols used to depict a Resistor. The symbol shown in Figure 1.2 for a resistor is generally preferred in Europe and some other parts of the world and will be used throughout this course. The symbol shown in Figure 1.3 is generally (but not always) used in the Americas.

11.What is the difference between independent and dependent active elements? Draw the symbols for all active elements.

An independent voltage source is characterized by a terminal voltage which is completely independent of the current through it

Another ideal source which we will need is the independent current source. Here, the current through the element is completely independent of the voltage across it

The two types of ideal sources that we have discussed up to now are called independent sources because the value of the source quantity is not affected in any way by activities in the remainder of the circuit. This is in contrast with yet another kind of ideal source, the dependent, or controlled, source, in which the source quantity is determined by a voltage or current existing at some other location in the system being analyzed.

Passive Element: The element which receives energy (or absorbs energy) and then either converts it into heat (R) or stored it in an electric (C) or magnetic (L ) field is called passive element.

Active Element: The elements that supply energy to the circuit is called active element. Examples of active elements include voltage and current sources, generators, and electronic devices that require power supplies

12.Demonstrate the shortcomings of the mathematical model for the voltage source used to represent a real physical system. Why is it valid only under certain conditions?

consider the model for the voltage source in Fig. I. 14a. We assume that the voltage source delivers V volts regardless of what is connected to its terminals. Theoretically, we could adjust the external circuit so that an infinite amount of current would flow, and therefore the voltage source would deliver an infinite amount of power. This is, of course, physically impossible. A similar argument could be made for the independent current source. Keep in mind that models have limitations and thus are valid representations of physical systems only under certain conditions

13.Demonstrate the shortcomings of the mathematical model for the current source used to represent a real physical system. Why is it valid only under certain conditions?

14.Describe dependent sources.

15. Ohm’s law.

16. Graphical representation of the voltage-current relationships for a linear and a nonlinear resistor.

non-linear

Non-Linear Circuit: Roughly speaking, a non-linear system is that whose parameters change with voltage or current.