Electrical Engineering 1


Teaching Aims

Atomic Nature of Electricity

Electricity is an invisible force that can produce heat, light and motion. Electrical properties of different materials are related to the structure of their atoms. All materials including solids, liquids and gases contain two basic particles with opposite polarities: the electron and the proton.

The polarity of the electron is negative while the polarity of the proton is positive. Each type of atom has certain number of electrons and protons that distinguishes it from the atom of all other elements.

Structure of the Atom

An atom is the smallest particle of an element possessing the unique characteristics of that element. Atoms have a planetary type of structure. They consist of a central nucleus surrounded by orbiting electrons.

The nucleus consists of positively charged protons and uncharged particles called neutrons. An atom has the same number of electrons and protons. Thus the atom is electrically neutral.

Valence Electrons

Electrons orbit the nucleus at certain distances from the nucleus. Each orbit corresponds to a certain energy level. The electrons in the outermost orbit are called valence electrons. They have higher energy and are less tightly bound to the atom than those closer to the nucleus.

If a valence electron acquires a sufficient amount of energy, it can escape from the outer orbit. The escaped valence electron is called a free electron. It can migrate easily from one atom to another.

Categories of Materials

When electrons can move easily from atom to atom in a material, it is conductive. Metals are good conductors. They have a large amount of free electrons. A material with a very few free electrons is an insulator. Insulators (dielectrics) cannot conduct electricity but can hold or store it.

Semiconductors conduct less than the conductors but more than the insulators. Because of their unique properties some of them are the basis for modern electronic devices such as diodes, transistors and integrated circuits.

Electric Chargen

Electricity is a physical phenomenon arising from the existence and interaction of electric charges.The quantity of electricity is the electric charge Q. The unit of charge is called Coulomb, symbolized by C. One coulomb is the total charge of 6.25·1018 electrons.

The electric charge has either negative or positive polarity, labeled -Q or +Q. Charges of opposite polarity attract. Charges of the same polarity repel.

Electric Field

The ability of an electric charge to attract or repel another charge is actually a physical force. The larger the charge, the greater the electric force. This force is called an electric field. It consists of invisible lines of force as shown in figure.

The electrical field between oppositely charged surfaces and the electric field around a stationary charge are illustrated as examples.

Voltage (Potential Difference)

Any charge has the potential energy to move another charge by either attraction or repulsion. The difference in the potential energy of two charges that move a certain number of electrons from one point to another is called potential difference or voltage.

Voltage is expressed as energy (W) divided by charge (Q) U = W/Q. The unit of voltage is the volt, symbolized by V. One volt equals one joule of energy required to move one coulomb of charge from one point to the other. Remember that voltage is potential difference between two points.

Voltage Sources

A DC voltage source is an energy source that provides a constant voltage. The battery converts chemical energy into electrical energy and creates a potential difference between two electrodes. The symbol of any DC voltage source with constant polarity is shown in the figure. The larger lines indicate the positive side.

DC power supply converts AC voltage from the power lines to a constant (DC) voltage regulated at various voltage levels. In most power supplies, a red jack is used for the positive terminal and a black jack for the negative.


Free electrons are available in all conductive and semi conductive materials. These electrons drift randomly in all directions within the material, as shown in the figure.

When a voltage is applied across the material, electrons start flowing from the negative to the positive side. Voltage is the driving force that causes a charge to flow. The free electrons in motion provide an electric current, symbolized by I.

Current Value

Current is measured by the number of electrons (having a charge, Q) that flow through the specific area per unit of time t. The unit of current is the ampere, A. One ampere of current results when one coulomb of charge passes through the given area in one second.

The current indicates the intensity of the charge in motion. With no voltage applied, there is no current. With more applied voltage, a larger amount of charge will pass a given point, which means a higher current.


When a current is present, the free electrons move through the material and occasionally collide with atoms. Because of these collisions, electrons lose some energy and their movement is restricted.

The property of the material that restricts the flow of current is called resistance, r. The unit of resistance is the ohm, symbolized by the Greek letter omega (Ω). Resistance is the opposition to current. Conductors have very little resistance; insulators have high resistance value.


Resistors are components specially designed to have a certain amount of resistance. The main applications of resistors are to reduce current or to divide voltage. Resistors can be either fixed or variable in value.

A fixed resistor has a resistance value that doesn't change. The most common type of fixed resistors includes carbon-composition, carbon-film, metal-film, wire-wound and surface mount chip resistors. The figure shows the shape and/or cross-section of several common types of resistors.

Resistor Color Code

Fixed resistors are color-coded to indicate their resistance value in ohms. The four-band color-code system is shown in figure.

The first three bands indicate the resistance value. It is calculated with two digits and a decimal multiplier, which gives the number of zeros after the two digits. The fourth band indicates the percent tolerance. A gold or silver third stripe indicates a fractional multiplier. Color codes for numerical values are listed in the table.

Variable Resistors

A variable resistor has a resistance that can be varied. Variable resistors are used to divide voltage and to control current. The figure shows the basic construction of a simple variable resistor. There is a circular disk of a resistive element inside the metal case. Terminals 1 and 2 have a fixed resistance between them. Terminal 3 is connected to a moving contact (wiper). By moving the contact the resistance between 1 and 3 (R13) or between 3 and 2 (R32) is varied.

Potentiometer & Rheostat

A potentiometer is a three-terminal variable resistor used to divide voltage. It is used as an adjustable voltage divider. Typical applications of a potentiometer are volume control for radio or TV receivers, or applied voltage control across load in a circuit.

A rheostat is a two-terminal device used to control current. A potentiometer can be used as a rheostat by connecting terminal 3 to either terminal 1 or terminal 2. Both symbols for a rheostat are equivalent.

Electric Circuit

An electric circuit is an arrangement of physical components that use voltage, current and resistance to perform some useful function. Basically an electric circuit consists of a voltage source, a load (with some resistance) and a closed path for current flow. In the figure, the battery is the voltage source, the lamp is the load, and the two conductors (wires) provide the current path.

Each circuit normally is represented by an associated schematic - a diagram that shows the interconnection of components using standard symbols.

Current Direction

The conventional current direction is from the positive side of the voltage source, flows through the external circuit and returns to the negative side of the voltage source. This is the direction that positive charges flow.

According to this convention, the electron current has the same direction even though electrons themselves move in the opposite way. Direct current has just one direction, as the DC voltage source has a fixed polarity.

Closed and Open Circuit

In a closed circuit, current can flow continuously in a complete current path. In an open circuit, the current path is broken so that there is no current.

Switches are commonly used for controlling the circuit path. Using he switch in the figure, the lamp can be turned on or off. The circuit is shown with associated schematics.

Play & Learn a Simple Circuit

Add and remove the connecting plugs from the bridging points by clicking between these points. Observe when the circuit is open or closed and see when the lamp is lit and when it is not.

Note that the plugs 2 to 3 and 4 to 5 are connected in "series" i.e. one after the other in the circuit, whereas plugs 4 to 5 and 6 to 7 are connected in "parallel", i.e. with equivalent ends connected to the same conductor.

Basic Circuit Measurement

A multimeter is used to measure voltage, current and resistance in an electric circuit. Meters with a printed scale and a moving pointer are called analog meters.

Adigital multimeter (DMM) provides a digital readout of the measurement quantity. In most DMMs, the proper range is automatically selected. Some DMMs also offer the ability to test capacitors, diodes, and transistors.

Current Measurement

To measure current through the resistor, the circuit must first be opened - by removing the connecting plug from the bridging points. The DMM must be set as an ammeter - the round function switch should be in the DC A position.

Connect the ammeter into the current path with polarity as shown - negative-to-negative, positive-to-positive. Otherwise, the ammeter readings will be negative (indicated by a minus sign). Such a connection is a series connection.

Voltage Measurement

Voltage is always measured relative to some other point in a circuit. Set the DMM as a voltmeter - the round function switch points to theDC V position. The voltmeter is connected across the component for which the voltage is to be measured. Such connection is a parallel connection.

The negative terminal of the meter must be connected to the negative side of the circuit, and the positive terminal of the meter to the positive side of the circuit. Otherwise the voltmeter readings will be negative.

Circuit Ground

In the wiring of practical circuits, one side of the voltage source is usually grounded. For electronic equipment, the ground just indicates a metal chassis or a large conductive area on a printed circuit board, which is used as a common or reference point. It is called the circuit ground. All the ground points in a circuit are electrically the same and are therefore common points.

All voltages in a circuit are referenced to ground unless otherwise specified. The figure gives a simple illustration of a grounded circuit and the ground symbol.

Voltage Measured to Ground

Voltage measurements made at a single point in a circuit are made relative to the earth (ground), and are assigned an "absolute" voltage of zero.

When voltages are measured with respect to ground, one of the meter leads is connected to the circuit ground, and the other to the point at which the voltage is to be measured. This is illustrated in the figure for several points in the circuit.

Resistance Measurement

To measure resistance, set the function switch on the DMM to ohms.(Ω). This way the DMM functions as an ohmmeter. The resistor must first be disconnected from the circuit - remove the connecting plugs from the bridging points. Then the ohmmeter is connected across the resistor. Polarity is not important.

Remember that infinite ohms mean an open circuit. In an open circuit the resistance is high but current is zero.

Simple Circuit Arrangement

Arrange a simple circuit consisting of a voltage source and a resistor. Connect the ammeter and the voltmeter in the proper place in the circuit to measure current and voltage across the resistor.

Ohm's Law

Ohm's law is one of the most important laws in the field of electricity and electronics. It gives the relationship between voltage, current and resistance in a circuit. Ohm's law states that the amount of current increases with more applied voltage but decreases with more resistance.

According to Ohm's law, voltage and current are linearly proportional. When applied voltage increases, the current also increases if the resistance in a circuit is constant.

Ohm's Law (Continued)

Ohm's law states that current varies directly with voltage and inversely with resistance.

When the resistance increases, the current decreases in value if the applied voltage is constant.

Equivalent Form of Ohm's Law

Ohm's law can also be stated in another way.

From I = U/R equivalent relationships U= IR and R = U/I can be found.

The circle diagrams in the figure provide a graphic aid for applying Ohm's law. It is a an easy way to remember the formulas.

Play & Learn a Volt-Ampere Characteristic

The Ohm's law formula states that U and I are linearly proportional for any one constant value of R. The graphical representation of U and I is called a volt-ampere (VA) characteristic.

If U is varied (from 0 V to 1.5 V in this case) for a fixed R, the VA characteristic is a straight line. Repeat the experiment again with resistors R2 and R3. To change the resistor's value click on the blinking star. Observe the slope of the graph for different resistors' values.

Power in an Electric Circuit

When there is a current through a resistor, heat is produced by the collision of electrons and atoms. The heat is evidence that energy is used in producing current. The power P characterizes the time rate of energy usage (or the time rate of doing work). The unit of electric power is the watt, W.

The electric power in watts is the product of volts and amperes. By using Ohm's law, equivalent expressions are derived. The three power formulas are also known as Watt's law.

Power Rating of Resistors

The power rating is the maximum amount of power that a resistor can dissipate without being damaged by excessive heat. The power rating depends on resistor construction, especially on physical size. The larger the physical size, the higher the power rating. The figure shows the relative size of carbon-composition resistors with different standard power ratings. There is no correlation between a resistor's physical size and its resistance value. Some typical wire wound power resistors are also shown. They can have ratings from 5 W up to 100 W or greater.

Series Circuit

In a series circuit, the components are connected with only one path for current through all of them. The current is the same at all points in a series circuit.

Components connected in series form a string - an end of each component is connected to an end of the next.

Total Series Resistor

The total resistance RT of a series circuit equals the sum of the individual resistances of each resistor for any number (n) of individual resistors connected in series.

RT = R1 + R2 + R3 + ... + Rn

The current in a series circuit is given by Ohm's law I=UT/RT, where UT is the voltage applied across the total resistance.

Voltage Source in Series

The total voltage of a series circuit is equal to the algebraic sum of the individual source voltages.

US(tot) = US1 + US2 + US3

The series voltage sources are added when their polarities are in the same direction and are subtracted when their polarities are in opposite direction.

Series Voltage Drop

The IR voltage across each resistance is called a voltage drop because it reduces the potential difference for the remaining resistance in the circuit. The polarity of a voltage drop is positive at the end of the resistor that is closest to the positive terminal of the voltage source.

The voltage drop across any of series resistors can be found from UR = IR, where I is the series current. Using the meter's readouts for current and voltage drops, determine the resistance value of each resistor.

Kirchoff's Voltage Law

Kirchoff's voltage law is a fundamental circuit law. It states that algebraic sum of all the voltages around a closed path is zero. In other words the same law states:

The sum of all the voltage drops around a closed path in a circuit is equal to the total source voltage. The figure illustrates a verification of Kirchoff's voltage law.

Play & Learn Kirchoff's Voltage Law

Measure the DC power supply voltage and the voltage drop across each resistor. Check if meter readings fulfill the Kirchoff's voltage law.

Voltage Dividers

A series circuit acts as a voltage divider. Since each resistor has the same current through it, the voltage drops are proportional to the resistance values.

The voltage drop across any resistor in a series circuit is equal to the ratio of that resistance value to the total resistance, multiplied by the source voltage. The voltage divider is used for setting the DC operating point (bias) in an amplifier.

Play & Learn Voltage Dividers

Calculate the voltage drop across each resistor using the voltage divider formula. Compare the calculated values with the measured ones.

Troubleshooting - Open Circuit

Open components and shorts between conductors are common problems in circuits. When a lamp or a resistor burns out, it causes a break in the current path and creates an open circuit. An open component in a series circuit prevents current flow.

When a series circuit is open, all of the source voltage appears across the open because without a currents, there can be no voltage drop across any of the others components.

Troubleshooting - Short Circuit

When there is a short, all of the current goes through the short. A portion of the series resistances is bypassed thus reducing the total resistances. As a result, the current increases. There is no voltage across the shorted part because a short circuit has practically zero resistance.

In order to troubleshoot a short, the voltage across each resistor can be measured until a reading of 0V is found.

Parallel Circuit

When two or more resistors are individually connected between the same two points, they are in parallel with each other. A parallel circuit provides more than one path for current. Each parallel path in a circuit is called a branch.

The voltage is the same across all branches in parallel circuit. Each branch has its own individual current. According to Ohm's law, the current in each parallel branch equals the applied voltage divided by each branch's resistance.

Kirchoff's Current Law

A node is any point in a circuit where two or more components are connected. Kirchoff's current law states that the total current into a node is equal to the total current out of that node. Kirchoff's current law can also be stated in this way: The algebraic sum of all currents entering and leaving a node is equal to zero.

The figure illustrates a verification of Kirchoff's current law. The total current is equal to the sum of all branch currents.

Total Parallel Resistance

For convenience, parallel resistors are designated by two parallel marks. For example, R1 in parallel with R2 can be written as R1 || R2. The total resistance RT is determined by the reciprocal formula. It is applied to any number of parallel resistors in any value. In case of n equal resistors with resistance R, RT = R/n. The total resistance of two resistors in parallel is equal to the product of the two resistors divided by the their sum. The RT of a parallel circuit is always less than the value of the smallest resistor.

Application Assignment

Determine the resistance value of the R3 resistor by observing the meter's readings.

Current Divider

A parallel circuit acts as a current divider since the total current divides among the parallel branches.

The branch currents are inversely proportional to the resistors value because the same voltage is applied across each resistor in parallel. The branch with the lowest resistance has the most current. If the voltage is known, then Ohm's law is used. If the total current is known the current divider formula is used.

Troubleshooting - Open Branches

The open branch circuit has no current and the lamp in this branch cannot light, but the other lamps operate normally. This example shows the advantage of wiring components in parallel compared to a series circuit.

To find an "open", the total current IT should be measured. When a parallel resistor is open, IT is always less than its normal value. If one of the resistors is open, the total current will equal the sum of currents in the good resistors.

Troubleshooting -Shorted Branches

A short circuit across a branch shorts out all the branches. There is no voltage across the shorted branches. Since there is not any current through the branches, the lamps cannot function.

The short-circuited components are not damaged, however, because there is no current. The circuit draws excessive current from the source because of the short circuit. To protect the wiring and the voltage source from damage, there should be a fuse in the circuit that opens with excessive current. The components can operate again when the circuit is restored to normal by removing the short circuit.

Series-Parallel Circuits

A series-parallel circuit consists of combinations of both series and parallel current paths. The figure shows an example of a simple series-parallel circuit. In the figure R1 is in series with parallel-connected R2 and R3. Series-parallel circuits are analyzed by applying known relationships for series and parallel circuits.

Analysis of Series-Parallel Circuit

Total resistance RT for series-parallel connection is obtained by R1+ R2 || R3· RT = R 1 + R23, where R23 = R2·R3/( R2+ R3). Total current IT = U/ RT. The voltage drops across resistors can be calculated using the voltage-divider principles. UR1 = U· (R1/ RT), UR2 = U· (R23/ RT). Voltages across R2 and R3 are equal because R2 || R3. Branch currents are: I2 = UR2 / R2; I3 = UR2 / R3. Compare calculated values with the measured ones.

Other Series-Parallel Circuits

The figures illustrate more complex examples of series-parallel connections. On the left, R1 is in parallel with the series connected R2 and R3. This entire combination is then in series with R6 || (R4 and R5).

On the right, R1 is in series with R2 || R3 and R4 || R5.