Basic EE Chapter 2

Basic Electrical Engineering Chapter 2

Kirchhoff’s Law

Kirchhoff's current law (1st Law) states that current flowing into a node (or a junction) must be equal to current flowing out of it. This is consequence of charge conservation. Kirchhoff's voltage law (2nd Law) states that the sum of all voltages around any closed loop in a circuit must equal zero.

Kirchhoff’s Current Law

Kirchhoff’s Current Law states that” the algebraic sum of all the currents at any node point or a junction of a circuit is zero”.

   Σ I = 0

Considering the above figure as per the 

Kirchhoff’s Current Law

i1 + i2 – i3 – i4 – i5 + i6 = 0 ……… (1)

The direction of incoming currents to a node is taken as positive while the

outgoing currents is taken as negative. The reverse of this can also be taken,

i.e. incoming current as negative or outgoing as positive. It depends upon your choice.

The equation (1) can also be written as

I1+i2+i6=i3+i4+i5

Sum of incoming currents = Sum of outgoing currents

According to the Kirchhoff’s current law, The algebraic sum of the currents

entering a node must be equal to the algebraic sum of the currents leaving

the node in an electrical network.

Kirchhoff’s Voltage Law

Kirchhoff’s Voltage Law states that the algebraic sum of the voltages (or voltage drops) in any closed path of network that is transverse in a single direction is zero or in other words, in a closed circuit, the algebraic sum of all the EMFs + the algebraic sum of all the voltage drops (product of current (I) and resistance (R)) is zero.

Σ E + Σ V = 0

The above figure shows closed circuit also

termed as a mesh. As per the

Kirchhoff’s Voltage Law

           -V1+(-V2)+iR1+iR2=0

Here, the assumed current I causes a positive voltage drop of voltage when

flowing from the positive to negative potential while negative potential drop

while the current flowing from negative to the positive potential.

       i(R1+R2)=V1+V2    

                 OR

       i=V1+V2/(R1+R2)

Considering the other figure shown below and assuming the direction of the

current i.

It is seen that the voltage V1is negative in both the equation (2) and the

equation (3) while V2 is negative in the equation (2) but positive in the

equation (3). This is because of the change in the direction of the current

assumed in both the figures. In the figure A, the current in both the source

V1 and V2 flows from negative (-ive) to positive (+ive) polarity while in figure

B the current in the source V1 is negative to positive but for V2 is positive to

negative polarity.

For the dependent sources in the circuit, KVL can also be applied. In case of

the calculation of a power of any source, when the current enters the source,

the power is absorbed by the sources while the source delivers the power if

the current is coming out of the source.

It is important to know some of the terms used in the circuit while applying

KCL and KVL like node, Junction, branch

Node

A node is a point in the network or circuit where two or more circuit elements

are joined. For example, in the above circuit diagram A and B is the node

points.

Junction

A junction is a point in the network where three or more circuit element are

joined. It is a point where the current is divided. In the circuit above B and D

are the junctions.

Branch

The part of a network, which lies between the two junction points is called a

Branch. In the above circuit DAB, BCD and BD are the branches of the

circuit.

Loop

A Closed path of a network is called a loop. ABDA, BCDB is loop in the above

circuit diagram shown.

                                    Mesh

Most elementary form of a loop which cannot be further divided is called a Mesh.

Generation of alternating emf

A voltage can be developed in a coil of wire in one of the three ways:

1. By changing the flux through the coil.

2. By moving the coil through the magnetic field.

3. By altering the direction of the flux with respect to the coil.

The first one is that voltage is said to be induced emf and in accordance with Faraday's law, its magnitude at any instant of time is given by the formula as

shown below:

e = N(dΦ/dt) x 10 -8 volts

where N is the number turns in a coil

dΦ/dt = rate at which the flux in maxwells changes through the coil.

Please take note that in this method of developing an emf, there is no physical

motion of coil or magnet; the current through the exciting coil that is

responsible for the magnetism is altered to change the flux through the coil in which the voltage is induced. For the second and third method mentioned above, there is actual physical motion of coil or magnet, and in altered positions of coil or magnet flux through the coil changes. A voltage developed on these ways is called a generated emf and is given by the

equation:

e = Blv x 10-8 volts

where B is the flux density in lines per square inch

l is the length of the wire, in., that is moved relative to the flux v is the velocity of the wire, in.per sec., with respect to the flux

The figure above illustrates an elementary a-c generator. The single turn coil may be

moved through the magnetic field created by two magnet poles N and S. As you can see, the ends of the coil are connected to two collectors upon which two stationary brushes rest on it. 

For the clockwise rotation as shown, the side of the coil on north pole N is moving vertically upward to cut the maximum flux under north pole N, while the other side of the coil on south pole S is moving vertically downward to cut the maximum flux under south pole S. After the coil is rotated one quarter of a revolution to the position as shown below:

the coil sides have no flux to be cut and no voltage is generated. As the coil proceeds

to rotate, the side of the coil on south pole S will cut the maximum flux on north pole

N. Then, the side of the coil previously on north pole N will cut the maximum flux on

south pole S. 

With this change in the polarity that are cut by the conductors, reversal in brush potential will occur. There are two important points that would like to

emphasize in connection with the rotation of the coil of wire through a fixed

magnetic field:

1) The voltage changes from instant to instant.

2. The electrical polarity (+) and minus (-) changes with alternating positions under

north and south poles.

In actual, ac generator rotate a set of poles that is placed concentrically within a

cylindrical core containing many coils of wires. However, a moving coil inside a pair

of stationary poles applies equally well to the rotating poles construction; in both

arrangements there is a relative motion of one element with respect to the other.

Difference between D.C & A.C

Electricity flows in two ways: either in an alternating current (AC) or in a direct

current (DC). 

Electricity or "current" is nothing but the movement of electrons through a conductor, like a wire. 

The difference between AC and DC lies in the

direction in which the electrons flow. 

In DC, the electrons flow steadily in a single

direction, or "forward." 

In AC, electrons keep switching directions, sometimes going "forward" and then going "backward."

Alternating current is the best way to transmit electricity over large distances.

What is AC power?

Alternating current (AC) power is the standard electricity that comes out of power outlets and is defined as a flow of charge that exhibits a periodic change in direction.

AC's current flow changes between positive and negative because of electrons—electrical currents come from the flow of these electrons, which can move in either a positive (upward) or negative (downward) direction. 

This is known as the sinusoidal AC wave, and this wave is caused when alternators at power plants create AC power.

Alternators create AC power by spinning a wire loop inside a magnetic field. Waves of alternating current are made when the wire moves into areas of different magnetic polarity—for example, the current changes direction when the wire spins from one of the magnetic field's poles to the other. 

This wave-like motion means that AC power can travel farther than DC power, a huge advantage when it comes to delivering power to consumers via power outlets.

What is DC power?

Direct current (DC) power, as you may suss from the name, is a linear electrical current—it moves in a straight line.

Direct current can come from multiple sources, including batteries, solar cells, fuel cells, and some modified alternators. DC power can also be "made" from AC power by using a rectifier that converts AC to DC.

DC power is far more consistent in terms of voltage delivery, meaning that most electronics rely on it and use DC power sources such as batteries. 

Electronic devices can also convert AC power from outlets to DC power by using a rectifier, often built into a device's power supply. A transformer will also be used to raise or lower the voltage to a level appropriate for the device in question.

Not all electrical devices use DC power, though. Many devices, household appliances, especially, such as lamps, washing machines, and refrigerators, all use AC power, which is delivered directly from the power grid via power outlets.

What's the need for two different power types?

Although many of today's electronics and electrical devices prefer DC power because of its smooth flow and even voltage, we could not get by without AC. Both types of power are essential; one is not "better" than the other.

In fact, AC dominates the electricity market; all power outlets bring power into buildings in the form of AC, even where the current may need to be immediately converted into DC power. This is because DC is not capable of traveling the same long distances from power plants to buildings that AC is. It is also a lot easier to generate AC than DC due to the way generators turn, and the system is on the whole cheaper to operate—with AC, power can be hauled through national grids via miles and miles of wire and pylons easily.

DC primarily comes into play, where a device needs to store power in batteries for future use. Smartphones, laptops, portable generators, torches, outdoor CCTV camera systems… you name it, anything battery-powered relies on storing DC power. When batteries are charged from the mains supply, AC is converted to DC by a rectifier and stored in the battery.

This is not the only method of charging used, though. If you have ever charged your phone using a power bank, for example, you are using a DC power supply rather than an AC one. In these situations, DC-DC power supplies may need to change the voltage of the output (in this case, the power bank) for the device's (in this case, the phone) use.