### 1.1 Conventional and electron current flow

In the battery,there are positive and negative poles. To make the battery works, we have to connect the positive and negative to make the potential difference by the electric current flow from high potential (positive charge) to low potential (negative charge).

Conventional current flow is the direction of the current flow in electric power technology which is from positive charge to negative charge. For the electron flow, it will flow in the opposite direction to the conventional current flow.

In the battery,there are positive and negative poles. To make the battery works, we have to connect the positive and negative to make the potential difference by the electric current flow from high potential (positive charge) to low potential (negative charge).

Conventional current flow is the direction of the current flow in electric power technology which is from positive charge to negative charge. For the electron flow, it will flow in the opposite direction to the conventional current flow.

### 1.2 Distinction between source and load

Every electrical device will have a source which stand for the delivery of electrical power and a load which is the one that absorb the power.

Every electrical device will have a source which stand for the delivery of electrical power and a load which is the one that absorb the power.

The way to classify which one is source and load is that we have to see the conventional current flow. For the source, the current will flow out from the positive terminal.On the other hands, for the load, the current will flow into positive terminal.

The way to classify which one is source and load is that we have to see the conventional current flow. For the source, the current will flow out from the positive terminal.On the other hands, for the load, the current will flow into positive terminal.

### 1.3-1.6 Sign notation

For electricity, the positive and negative signs use to tell the direction. If you set one direction to be positive, the opposite direction will be negative.

For electricity, the positive and negative signs use to tell the direction. If you set one direction to be positive, the opposite direction will be negative.

For voltage, there are double subscript notation to tell the potential difference and the polarities.

For example, potential from A to B is +50V , it means that A is positive respect to B because the current flows from A to B as you see from the potential difference. If the value of potential difference is negative, it means that at node A has lower potential than node B.

#### The same for current, it also use positive and negative sign to show the flow direction.It you fix one direction to be positive, you will know that the opposite direction will be represent in negative sign.

### 1.7 Graph of an alternating voltage

The graph of an alternating voltage is the alternating voltage represent by the means of a graph. It means that you use the voltage value to draw the graph which x-axis is the time and y-axis is the voltage. From the graph, the negative region means that it has negative voltage ( changing in the direction of the positive and negative terminals).

The graph of an alternating voltage is the alternating voltage represent by the means of a graph. It means that you use the voltage value to draw the graph which x-axis is the time and y-axis is the voltage. From the graph, the negative region means that it has negative voltage ( changing in the direction of the positive and negative terminals).

### 1.8-1.9 Sinusoidal Voltage

** **For ac voltage generation, the graph is nearly a perfect sine wave which can represent in the formula

**e=Emcos(2πft+θ)**

** **e= instantaneous voltage (v) t=time(s)

Em= amplitude (peak value of voltage) θ=fixed angle (rad)

f= frequency (Hz)

** **

** **For ac voltage generation, the graph is nearly a perfect sine wave which can represent in the formula

**e=Emcos(2πft+θ)**

** **e= instantaneous voltage (v) t=time(s)

Em= amplitude (peak value of voltage) θ=fixed angle (rad)

f= frequency (Hz)

** **

To convert cosine function to sine function is to add right angle to the sine function because sine function and cosine function have phase difference 90 degree.

sine function and cosine function have phase difference 90 degree.

To convert cosine function to sine function is to add right angle to the sine function.

sine function and cosine function have phase difference 90 degree.

To convert cosine function to sine function is to add right angle to the sine function.

### 1.10 Effective value of an ac voltage

For ac voltage, it is better to use effective voltage value for voltage that varies sinusoidally.

For ac voltage, it is better to use effective voltage value for voltage that varies sinusoidally.

The rms or effective voltage or current is the value that converts the same energy as does a dc value.

In other words, the effective value is an equivalent DC value which tells you how many volts or amps of DC that a time-varying sinusoidal waveform is equal to in terms of its ability to produce the same power.

The rms or effective voltage or current is the value that converts the same energy as does a dc value.

In other words, the effective value is an equivalent DC value which tells you how many volts or amps of DC that a time-varying sinusoidal waveform is equal to in terms of its ability to produce the same power.

The relationship between the effective value and maximum value are shown in the form of formula:

Eeff = Em/√2 Ieff = Im/ √2

Sometimes, effective voltage value called RMS or root mean square. It also use to measure of heating effect compare to dc voltage. Additional, most of the electrical equipment such as ammeters and voltmeters measure both current and voltage in effective value.

### 1.11 Phasor representation

We will not concern much with the instantaneous value because voltage is measured in the effective value and also phase angles rather than the maximum voltage value.

We will not concern much with the instantaneous value because voltage is measured in the effective value and also phase angles rather than the maximum voltage value.

The phasor diagram is to show the magnitude and phase angles between voltages and currents. Phasor is similar to a vector with the arrow because it shows both magnitude and also the direction in the form of angle. The angle between 2 phasors is equal to the electrical phase angle between the quantities.

The phasor diagram is to show the magnitude and phase angles between voltages and currents. Phasor is similar to a vector with the arrow because it shows both magnitude and also the direction in the form of angle. The angle between 2 phasors is equal to the electrical phase angle between the quantities.

**There are some rules for the phasor :**

- Phasors in phase means that they are parallel and go in the same direction with no phase angle.
- Phasors out of phase are when phasors point in the different directions and there are some phase angle.
- Phasor rotate clockwise is said to be a lead phasor. On the other hands, the phasor will be a lag phasor if it rotate counterclockwise.
- Phasors do not have to start from a common origin to show their magnitudes and phase relationship.
- If one phasor has lag angle to another phasor when it rotates clockwise to be in phase with another phasor but it will be still some lag angle between them.

**There are some rules for the phasor :**

- Phasors in phase means that they are parallel and go in the same direction with no phase angle.
- Phasors out of phase are when phasors point in the different directions and there are some phase angle.
- Phasor rotate clockwise is said to be a lead phasor. On the other hands, the phasor will be a lag phasor if it rotate counterclockwise.
- Phasors do not have to start from a common origin to show their magnitudes and phase relationship.
- If one phasor has lag angle to another phasor when it rotates clockwise to be in phase with another phasor but it will be still some lag angle between them.

### 1.12 Harmonics

Harmonics are the signal that come to distort the main signal and make the form of the graph change from the original. This distortion can be produced by magnetic saturation in the core of transformer or by the switching action of thyristors in the electronic drives.

For example of 2 sources in the same series circuit with different voltage, it will result the terminal voltage wave in the form of flat-topped wave which is the non-sinusoidal waveform whose degree of distortion depends on the magnitude of the harmonic it contains.

For example of 2 sources in the same series circuit with different voltage, it will result the terminal voltage wave in the form of flat-topped wave which is the non-sinusoidal waveform whose degree of distortion depends on the magnitude of the harmonic it contains.

A square wave is composed of a fundamental wave and an infinite number of harmonics. The higher harmonics have smaller and smaller amplitude. However, these high-frequency harmonics produce the steep sides and pointy corners of the square wave. In practical way, square waves are not produced by adding sine waves but any wave shape can be built up from a fundamental wave and the number of harmonics.

In ac circuit, the fundamental current and fundamental voltage together produce fundamental power which is the useful power that cause power to rotate. The product of a harmonic current also produces a harmonic power. Additional, the product of a fundamental voltage and a harmonic current yields zero net power.

### 1.13 Energy in an inductor

The energy store in the coil in its magnetic field when it has a current I is given by the formula:

where

W = energy storing (J)

L= inductance of the coil (H)

I = current (A)

### 1.14 Energy in the capacitor

A capacitor will store the voltage when a voltage appears across its terminals. The energy is given by

where

W= energy stored in the capacitor (J)

C= capacitance of the capacitor (F)

E= voltage(V)

### 1.15 Some useful equations

The image above is the set of the equations that use to analyst the common AC circuit which will be useful to compose the impedances to be easy for calculation.

The image above is the set of the equations that use to analyst the common AC circuit which will be useful to compose the impedances to be easy for calculation.

### 1.16 Magnetic field intensity H and flux density B

** **The presence of magnetic flux intensity is given by the formula

H=U/I

Where

H= magnetic field intensity (A/m)

U = magnetomotive force acting on the component (A)

l = length of the component (m)

The formula for the flux density is

B=Φ/A

Where

B = flux density (T)

A= cross section of the component (m2)

Φ= flux in the component (Wb)

There are the relationship between the flux density (B) and the magnetic field intensity is represented graphically by B-H curve of the material.

### 1.17 B-H curve of vacuum

The B-H curve of vacuum is a straight line. A vacuum never saturates, no matter how great the flux density may be. For nonmagnetic material such as copper, paper, rubber,and air have B-H curves almost identical to the vacuum.

The B-H curve of vacuum is a straight line. A vacuum never saturates, no matter how great the flux density may be. For nonmagnetic material such as copper, paper, rubber,and air have B-H curves almost identical to the vacuum.

In vacuum, the magnetic flux density B is directly proportional to the magnetic field intensity H, and it shows in the equation

B=μoH

Where

B= flux density (T)

H= magnetic field intensity (A/m)

μo = magnetic constant =(4∏ x10-7)

### 1.18 B-H curve of the magnetic material

The flux density of the magnetic material depends on the magnetic field intensity and its value is given by

B=μoμrH

where

B= flux density (T)

H = magnetic field intensity (A/m)

μo= magnetic constant

μr= relative permeability of the material

Different magnetic material will have different typical saturated curve because the value of μr is not constant so it makes the graph not linear.

### 1.19 Determining the relative permeability

The relative permeability of the material is the ratio of the flux density in the material to the flux density that would be produced in vacuum under the same magnetic field intensity (H).

The relative permeability of the material is the ratio of the flux density in the material to the flux density that would be produced in vacuum under the same magnetic field intensity (H).

There are the approximate equation to find the relative permeability

μo = 80,000B/H

where

B= flux density in the magnetic material (T)

H= corresponding magnetic field intensity (A/m)

There are the approximate equation to find the relative permeability

μo = 80,000B/H

where

B= flux density in the magnetic material (T)

H= corresponding magnetic field intensity (A/m)

As the magnetic field intensity increases, the magnetic material saturated more and more and all B-H curves follow the B-H curve of the vacuum.

As the magnetic field intensity increases, the magnetic material saturated more and more and all B-H curves follow the B-H curve of the vacuum.

### 1.20 Faraday’s law of electromagnetic induction

Faraday’s law of electromagnetic induction is the law of electromagnetism that represent the relationship between the voltage and flux in the circuit.

Faraday’s law of electromagnetic induction is the law of electromagnetism that represent the relationship between the voltage and flux in the circuit.

**Faraday’s law states:**

- If the flux linking a loop (or turn) varies as a function of time, a voltage is induced between its terminals.
- The value of the induced voltage is proportional to the rate of the change of the flux.

**Faraday’s law states:**

- If the flux linking a loop (or turn) varies as a function of time, a voltage is induced between its terminals.
- The value of the induced voltage is proportional to the rate of the change of the flux.

Faraday’s law states:

- If the flux linking a loop (or turn) varies as a function of time, a voltage is induced between its terminals.
- The value of the induced voltage is proportional to the rate of the change of the flux.

By the definition, when the flux inside the loop varies at the rate of 1 Wb/sec, a voltage 1V is induced between its terminals. If the flux varies inside a coil of N turns, the voltage induced is given by:

E = N(∆Φ/∆t)

where

E= induced voltage (V)

N= number of turns in the coil

∆Φ= change interval during which the flux change (s)

∆t = time interval during which the flux change (s)

By the definition, when the flux inside the loop varies at the rate of 1 Wb/sec, a voltage 1V is induced between its terminals. If the flux varies inside a coil of N turns, the voltage induced is given by:

E = N(∆Φ/∆t)

where

E= induced voltage (V)

N= number of turns in the coil

∆Φ= change interval during which the flux change (s)

∆t = time interval during which the flux change (s)

Faraday's law of electromagnetic induction is the basis of operation of transformers, generators ,and alternating current motors.

Faraday's law of electromagnetic induction is the basis of operation of transformers, generators ,and alternating current motors.

### 1.21 Voltage induced in the conductor

In many motors, the coils move with respect to a flux that is fixed in space. The relative motion produces a change in the flux linking the coils and a voltage induced according to Faraday’s law.

There are the special case to calculate the induced voltage with reference to the conductors rather than the coil itself. The value of the induced voltage is given by

E= B/v

where

E= induced voltage (V)

B= flux density (T)

I = active length of the conductor in the magnetic field (m)

v= relative speed of the conductor (m/s)

There are the special case to calculate the induced voltage with reference to the conductors rather than the coil itself. The value of the induced voltage is given by

E= B/v

where

E= induced voltage (V)

B= flux density (T)

I = active length of the conductor in the magnetic field (m)

v= relative speed of the conductor (m/s)

### 1.22 Lorentz force on a conductor

Lorentz force or electromotive force is when a current caring conductor is placed in a magnetic field and cause this force to happen. This force is of fundamental importance because is the basic structure of the operation of the motors and generators of many electrical instrument.

** ** The magnitude of the force is depends on the orientation of the conductor respect to the field.The force is greatest when the conductor is perpendicular to the field and zero when it is parallel to it. Between these two extremes, the force has intermediate values.

The maximum force acting on the straight conductor is given by:

F=BlI

where

F= force acting on the conductor (N)

B= flux density of the field (T)

l= active length of the conductor (m)

I= current in the conductor (A)

### 1.23 Direction of the force acting on a straight conductor

Whenever a conductor carries a current. It is surrounded by a magnetic field. For a current flow in to the page, the circular lines of force have the direction. The figure below shows the magnetic field created between the N,S poles of a powerful permanent magnet.

However, the magnetic field does not. Because as you can see from the figure because lines of force never cross each other.

The lines of force created by the conductor and the permanent magnet act in the same direction above the conductor and in the opposite directions below it. These make the magnetic field change the shape. Additional, the line of flux act like stretched elastic bands. It tends to push it downward.

### 1.24 Residual flux density and coercive force

**Residual flux density and coercive force **

the coil surround a magnetic material formed in the shape of the ring. A current source, connected to the coil will form a current whose value and direction can be change.

This picture shows the method of determining B-H properties of magnetic material.

**Residual flux density and coercive force **

the coil surround a magnetic material formed in the shape of the ring. A current source, connected to the coil will form a current whose value and direction can be change.

This picture shows the method of determining B-H properties of magnetic material.

If you see from B-H curve,when the current increase B and H will be increase until it reach Bm and Hm which are maximum magnetic flux density and magnetic field strength.

If current is gradually reduced to zero the graph will not follow the same line as it increase because as we reduce the magnetic field intensity, the magnetic strength is influenced by the field Hm to remain original orientation. This phenomenon is called hysteresis.H is reduced to zero but the substantial flux density remain is called residual induction.

If we want to eliminate the residual flux, we have to reverse the current in the coil and gradually increase H in the opposite direction. When you reverse it until magnetic flux density become zero , this magnetic field intensity called coercive force.

In reducing the flux density from residual induction to zero, we will gain a furnish energy. This energy is used to overcome the frictional resistance of the magnetic domains as they oppose the change in orientation. This energy is in the form of heat, it will make the ring temperature rise.

### 1.25 Hysteresis loop

**The Hysteresis Loop and Magnetic Properties**

A great deal of information can be learned about the magnetic properties of a material by studying its hysteresis loop. A hysteresis loop shows the relationship between the induced magnetic flux density (**B)** and the magnetizing force **(H).** It is often referred to as the B-H loop.

Transformers and most electric motors operate on the alternating current. In the devices, the flux in the iron changes continuously both in value and direction. It will have both positive and negative residual induction and coercivity which we called this BH curve as hysteresis loop.

### 1.26 Hysteresis loss

The work was done by the magnetising force against the internal friction of the molecules of the magnet, produces heat. This energy which is wasted in the form of heat due to hysteresis is called **Hysteresis Loss. **When in the magnetic material magnetisation force is applied, the molecules of the magnetic material are aligned in one particular direction, and when this magnetic force is reversed in the opposite direction, the internal friction of the molecular magnets opposes the reversal of magnetism resulting in Magnetic Hysteresis.

To wipe out or overcome this internal friction or in other words known as residual magnetism, a part of the magnetising force is used. This work, done by the magnetising force produces heat; this wastage of energy in the form of heat is termed as **hysteresis loss.**

### 1.27 Hysteresis losses caused by rotation

Hysteresis losses are also produced when a piece of iron rotates in a constant magnetic field.

An armature AB, made of iron that revolves in a field produced by permanent magnets N and S. The magnetic domains in the armature tend to line up with the magnetic field. As the armature rotates, the N poles of the domains point first toward A and then toward B. Hysteresis losses are produced just as they are in an ac magnetic field.

### 1.28 Eddy current

There are an ac flux that link a rectangular-shaped conductor.According to Faraday's law, an ac voltage E1 is induced across its terminals. If the conductor is short-circuited, the alternating current will flow, it makes the conductor temperature increase.

If the second conductor is placed inside the first, a smaller voltage is induced because it links a smaller flux. As you can see from the picture, the short- circuit current I2 is less than I1 which is the power dissipated in this loop. A currents are progressively smaller as the area of the loops surrounding the flux decreases.

The ac flux passes through a solid metal plate is basically equivalent to a densely packed set of rectangular conductors touching each other. There are currents swirl back and forth inside the plate which is called eddy currents.

Consequently, a metal plate that is penetrated by an ac flux can become very hot.so, you should take care of the transformers not to get overheat.

Due to the Lenz's law, the eddy currents flow in such a way as to oppose the increasing flux.

### 1.29 Eddy currents in a stationary iron core

For all ac motors and transformers, there are a problem to eddy current when iron has to carry an ac flux. Because of the carrying of ac flux in the solid iron, the core can become overheat due to the eddy current losses. We can reduce the losses by splitting the core in two along its length because the voltage induced in each section is one half of what it was before. These will make the eddy current losses considerably reduced. The more you divide the iron core, the more losses decreasing.

In practice, in the core, there are the stacked lamination which is a small amount of silicon. It will alloy with steel to increase the resistivity to reduce the losses of eddy current. Therefore, we can conclude that eddy current losses decrease in proportion to the square of the number of laminations.

### 1.30 Eddy-current losses in a revolving core

The stationary field in direct-current motor and generator produce dc flux. This flux induces eddy currents in the revolving armature.

From the figure, there are the cylindrical iron core between the magnet. As it turns, the core cut the flux lines. From Faraday's law, a voltage is induced along its length having a polarities. It makes large eddy currents flow in the core because the resistance of the core is very low. These eddy currents produce large power loss in the form of heat. This power is proportional to the square of the speed and the square of flux density.

From the figure, there are the cylindrical iron core between the magnet. As it turns, the core cut the flux lines. From Faraday's law, a voltage is induced along its length having a polarities. It makes large eddy currents flow in the core because the resistance of the core is very low. These eddy currents produce large power loss in the form of heat. This power is proportional to the square of the speed and the square of flux density.

In conclusion, to reduce the eddy current losses, we laminate the armature suing thin circular laminations that are insulated from each other. The lamination will stack with the flat side running parallel to the flux line.

In conclusion, to reduce the eddy current losses, we laminate the armature suing thin circular laminations that are insulated from each other. The lamination will stack with the flat side running parallel to the flux line.

### 1.31 Current in an inductor

In inductive circuit, the voltage and current are related by the equation:

e= L∆i/∆t

Where

e = instantaneous voltage induced in the circuit (V)

L = inductance of the circuit (H)

∆i/∆t = rate of change of current (A/s)

This equation enables to calculate the instantaneous voltage when we know the rate of change of current.

However, when we want to calculate the current and we know the instantaneous voltage, it hards to calculate as you can see from the formula, it needs advanced mathematics to solve. We can use graphical method called volt- second method to solve. graphical method will show the trend of increasing and decreasing of the current with time in the response of voltage.

From the figures, the voltage applied across the inductance. If the inductance has the current I1 at time t1 and we want to determine the current in the short time.

If you want to calculate the current at time t2 when t2 is many change of time from t1. We have to increase the incremental changes in current during a long period (t2-t1).

The net area A after time interval T is equal to (A1-A2) volt-seconds.

To generalize, the current after interval always given by the formula

I = I1+A/L

where

I1 = current at start interval T

I = current after time interval T

A= net area under voltage curve during time T

L = inductance

Consider the inductance having negligible resistance connected to the source which voltage is according to the curve in the figure below.

If the initial current is zero, the value at t1 equal to I=A1/L. As time goes by the current increase in the same direction as the area under curve increase.However, when the current reaches the maximum at t2 the area cannot increase anymore so it starts to be negative. At t3 the area will include A1 and A2 also A3 in the negative way. So at t3, I=(A1+A2-A3)/L. At the same time, at t4 it will include area 4 in the negative sign same as A3.

From another graph, you will see that the graph is charged between t1 to t2 and discharged from t2 to t4 which this characteristic is similar to the capacitor.

If the current at the beginning of interval T is not zero, we simply add the initial value to all the ampere values calculated by the volt-second method.

### 1.32 Kirchhoff's voltage law

Kirchhoff's voltage law states that that the algebraic sum of the voltages around a close loop is zero. In the closed circuit, Kirchhoff's voltage law means that the sum of the voltage rises is equal to the sum of the voltage drops.

Kirchhoff's voltage law states that that the algebraic sum of the voltages around a close loop is zero. In the closed circuit, Kirchhoff's voltage law means that the sum of the voltage rises is equal to the sum of the voltage drops.

Voltages can be expressed in either double-subscript or sign notation. If the current go from positive sign to negative sign, the voltage will represent in positive sign but if it goes in the opposite direction, voltage will represent in negative sign.

Voltages can be expressed in either double-subscript or sign notation. If the current go from positive sign to negative sign, the voltage will represent in positive sign but if it goes in the opposite direction, voltage will represent in negative sign.

### 1.33 Kirchhoff's voltage law and double-subscript notation

Because voltage is an "across" variable and exist between 2 points, the double-subscript notation defines differences in potential.

The double- subscript notation Vab specifies point as a high potential. If this is not the case, the negative sign must be associated with the magnitude of Vab.

Note that Vab is the voltage at point A respect to point B.

From the figure below, there are six circuit elements connect in the close loop. In going around the circuit loop, we can start with any node and move either clockwise or counterclockwise direction until we come back to the starting point.

The set of voltages designated by the KVL equations may be ac or dc. If they are in ac, the voltage will represent in the form of phasors, having certain magnitudes and phase angles.

### 1.34 Kirchhoff's current law

Kirchhoff's current law states that the algebraic sum of currents that arrive at a point is equal to zero. It means that the sum of the current that flow into a terminal is equal to the sum of the currents that leave it.

### 1.35 Currents, impedances,and associated voltages

Consider the impedance Z carrying a current I, connect between 1 and 2. A voltage E12, having a magnitude IZ will appear across the impedance. However, there are the question about voltage across E12 equal to IZ or -IZ.

From the rule, you know that when moving across an impedance Z in the same direction as a current flow I, the voltage IZ will be positive sign. In the opposite way, if it goes against the current flow, the voltage IZ will represent in the negative sign. The current can be both dc or ac,and impedance can be resistive(R), inductive(jX1), or capacitive (-jXc).

In the most circuits, it is impossible to predict the actual direction of current flow in the various circuit elements. For example below, there are 2 known voltage sources E13 and E24 are connected to 4 impedances. Because the actual directions of current flows are presently unknown, we will assume arbitrary directions.

### 1.36 Kirchhoff's law and ac circuits

The same basic rules of writing double-subscript equations can be applied to ac circuits, including 3-phase circuits The only difference is that the resistive elements in dc circuits are replaced by resistive, inductive, or capacitive elements. Also, the voltages and currents are expressed as phasors which having both magnitude and angle.

### 1.37 KVL and sign notation

Voltage in ac and dc circuits are frequently indicated with sign notation and designed by symbols such as E1, Ea,em,and so on. As we cruise around the loop, we observe the polarity of the first terminal of every voltage we meet. If only the positive terminal of the voltage source is marked, the unmarked terminal will be negative. The polarity will be use to write KVL equation.

### 1.38 Solving ac and dc circuits with sign notation

In circuits using sign notation, we treat the IZ voltages in the same way as in circuits using double-subscript notation. The IZ voltage across an impedance Z is preceded by a positive sign whenever we move across the impedance in the direction of current flow and it will be negative if it goes the the opposite direction as the current flow.

### 1.39 Circuits and hybrid notation

In some circuits, it is useful to employ both sign notation and double-subscript notation.

### Exercise 1

- In phase means that one phasor is the part of another phasor
- out of phase means two phasors go in the different direction.
- Lead phase can be checked by looking at the magnitude of the phasor.
- Lag phase can be checked by rotate clockwise and in phase with another phasor.

### Exercise 2

- Conventional current flow is the direction of current flow in electric power technology.
- You can tell that it is the source by seeing the current flow out of the positive terminal.
- The difference in potential caused by the electron at the negative terminal compare to the positive terminal.
- Electron and electricity flow in the same direction in the electrical circuit.

### Exercise 3

- increase magnetic flux density
- reverse current
- increase resistance
- increase magnetic field intensity in the opposite direction
- reduce the flux density
- increase induced voltage

### Exercise 4

Hint: there are 2 ways to reduce the eddy current in the iron core.

Hint: there are 2 ways to reduce the eddy current in the iron core.

- Make the conductor become laminates.
- increase the size of the iron core
- mix silicon and steel to the iron core
- reduce the air gap between the core
- increase the cross-sectional area of the core
- increase the volume of the core

### Exercise 5

- The sum of current in the close loop equal to zero.
- current that pass every resistance in the circuit will be equal.
- Voltage around the close loop equal to zero.
- current in the parallel circuit will equal to the current in series circuit.

### Exercise 6

#### Hint: use the formula of voltage induced in a conductor.

- 10V
- 20V
- 30V
- 40V

A conductor 2m long moves at a speed of 60km/h through a magnetic field having a flux density of 0.6 T. Calculate the induced voltage.

### Solution E.6

### Exercise 7

- 1.8V
- 1.25V
- 1.35V
- 1.67V

A coil having 200 turns links a flux of 3mWb, produced by a permanent magnet. The magnet is moved,and the flux linking the coil falls to 1.2m Wb in 0.2s. Calculate the average voltage induced.

### Solution E.7

### Exercise 8

- 600N
- 200N
- 100N
- 300N

A conductor 3 m long carrying a current of 200A is placed in a magnetic field whose density is 0.5T. Calculate the force acting on the conductor if it is perpendicular to the lines of force.

### Solution E.8

### Exercise 9

- a. 6A b. 200 V c. 1660W d. 3124 W
- a. 12A b. 169.7 V c. 1440 W d. 2880 W
- a. 8A b. 170.65 V c. 2567 W d. 1367 W
- a. 5A b. 143.29V c. 1329 W d. 1236 W

A sinusoidal voltage of 120 V is applied to a resistor 10 ohms. Calculate

- a. the effective current in the resistor
- b. the peak voltage across the resistor
- c. the power dissipated by the resistor
- d. the peak power dissipated by the resistor

### Solution E.9

### Exercise 10

- I1=3A I2=2A I3=5A
- I1=1.9A I2=-2.7A I3=4.87A
- I1=1.43A I2=4A I3=-5.43A
- I1=-1.25A I2=2.32A I3=-7.87A

Calculate the currents in this circuit.