1. Dr. Cynthia Furse University of Utah
Introduction to Electrical & Computer Engineering Circuit Representation
Dr. Cynthia Furse
University of Utah

2. Introduction to Electrical Engineering Circuit Representation
Voltage, Current, Resistance
Ground / Reference / Neutral
Variable Resistors / Resistive Sensors
Measuring V,I,R
Series & Parallel elements
Node, Path, Loop

3. Voltage (DC) V I I I + + - - - V V V DC DC DC DC DC DC
Voltage and current are the fundamental elements of electricity. This card represents voltage sources that are constant, that output current that is also constant. We call these ‘direct current’ or DC sources. DC means the voltage (or current) is constant.
A battery is a good example of this kind of voltage. Voltages have positive (+) and negative (-) polarities, shown here. The current also has a polarity, shown by the direction of the arrow. The arrow always comes OUT of the positive terminal of the battery. The TAIL of the current is (-) and the arrowhead of the current is (+).
Note that there cards are set up so the black border indicates the side you would see physically. The sides with the red border indicate what you would see in a circuit diagram. There are two common ways of showing VDC in a circuit diagram, for instance.
ELECTRICAL ENGINEERING is all about ‘What can you do to a voltage (or current)?’ - V V V DC DC DC

4. Ground / Reference / NeutralV V
ref(erence)
= 0V
= ground
ref(erence)
= 0V
= ground
Voltage is always defined relative to a ‘ground’ or reference point. In a house, for example, the electrical system is grounded to ‘earth ground’. This is also sometimes called the ‘neutral’ point in the circuit. A copper rod (or several) are driven into the earth outside of the house, and are connected to the electrical system with heavy copper wire. The voltage at the ground point is ‘zero’. All current flows into this ground point. Two common symbols for ground are shown here. You will always need to ONE of these ground reference points in your system. All voltages will then be calculated relative to this point.

5. ̴ Voltage (AC) V V + + - V AC AC
This card represents voltage sources that are time varying. One type of time varying voltage is sinusoidal. We call these ‘alternating current’ or AC. AC means the voltage (or current) is sinusoidal. A 60 Hz (in the US) or 50 Hz (in Europe) electric outlet is a good example of this kind of voltage. Voltages have positive (+) and negative (-) polarities, shown here. AC voltages are normally shown in a circuit as having a ‘squiggly’ line in a circle, with or without a ‘V’ in the circle as well.
A 120 V electric outlet, such as the one shown here, has a short right slot and a long left slot, with a round-ish hole below them. The right slot is the ‘hot’ or positive side. The left slot is the ‘neutral’. The round hole is the ‘ground’.
About the colors of wires on these cards: The red lines represent the ‘positive’ , and the black represents negative or ground. In reality, if you are hooking up an electrical outlet with romex, the positive or ‘hot’ side is normally black (or red wire (and usually a gold screw). The ‘neutral’ is normally white (with a silver screw). The ‘ground’ is normally uninsulated copper wire (with a green screw). The neutral and ground are supposed to be electrically the same, but they each serve a special safety purpose. Back at the circuit breaker box, the neutral and ground are connected together, and go to the ground rods below the house. But at the appliance, such as a washing machine, for instance, the ground is connected directly to the metal chassis, usually with a green screw, and the neutral is connected to the ‘ground’ point of the circuit board that runs the motor and control system. Just in case there is an electrical short, where a positive voltage comes in contact with the metal chassis, the ground carries the resulting current back to the earth ground rods. This keeps it from shocking a person who might touch the chassis. Major appliances and power tools generally have three prong plugs. Two prong plugs do not have this extra protection for a short circuit to the chassis and are generally used only for small electrical devices that have plastic exteriors. V AC

6. Resistor
Voltage and current are the fundamental elements of electricity. Resistance relates voltage and current through the familiar ‘Ohm’s Law’. V= I R.
Resistors work the same way whether the voltage and current are AC or DC. There is no polarity associated with a resistor, only with the voltages and currents. There is also no right or wrong ‘side’ to a resistor. You can turn them around (top to bottom, in this picture), and they act just the same.
The colored bands on the resistor are a code for the value of resistance and its tolerance. See ‘Resistor Color Code’ in the reference material for more information.
Remember on our first card, I said ‘ELECTRICAL ENGINEERING is about what you can do to a voltage (or current)?’ So … if you have a fixed voltage (like a battery), and you change the resistance, you will then change the current.
R (Ω)
R (Ω)

7. Variable Resistor / Resistive Sensor
Variable Resistor. See page 44 of your textbook.
On our last card, we said that if you have a fixed voltage, changing the resistance can change the current. Or if you have a fixed current, you can change the voltage. Resistance relates voltage and current through the familiar ‘Ohm’s Law’. V= I R. So, selecting / controlling / changing the resistance is one way that we control the voltage or current in our circuits.
There are several ways to control the resistance.
Choose a resistor value (see standard resistor values in the reference material)
Use a variable resistor, and ‘dial’ the resistance you want. (
Potentiometer: 3-terminal variable resistor. Connect to the middle and one side leg. The two outside legs will be the full resistance, regardless of where the dial is set.
Rheostat: 2-terminal variable resistor
There are also several types of sensors where the resistance changes depending on what you are trying to sense.
Temperature – Thermister
Pressure – Piezoresistor
Light intensity – Light-dependent R (LDR)
Thank you to the following website for the picture of how a round potentiometer works:
R (Ω)

8. Resistance Standard Resistor Values Variable resistor Resistive Sensor
Potentiometer: 3-terminal variable resistor. Rheostat: 2-terminal variable resistor
Resistive Sensor
Temperature – Thermister
Pressure – Piezoresistor
Light intensity – Light-dependent R (LDR)

9. Measuring Voltage (Voltmeter) DVM = Digital VoltMeterDC
voltmeter
AC (RMS)
voltmeter + + + ̴
VΩ com A
Measuring Voltage. Yellow is a common color for handheld electrical measurement equipment, because it can be seen. This card represents a Digital Voltmeter (DVM). When you plug in the cables as shown, you can measure voltage (V) or resistance (Ω). The voltmeter has a dial (not shown) that dials between measuring DC voltage and AC voltage. When measuring AC voltage, the value shown will be RMS (root mean square). Note that it matters which side is + and which is -. If you reverse the leads, the voltage you measure will also be reversed (inverted or ‘minus-ed’). - V DC - V AC -
RMS
DVM

10. Measuring Resistance (Ohmeter)Ω
VΩ com A
Measuring Resistance. (Another Yellow Measurement card) This card represents a Digital Voltmeter (DVM). When you plug in the cables as shown, you can measure voltage (V) or resistance (Ω). The voltmeter has a dial (not shown) that dials to measure resistance. When measuring resistance, it doesn’t matter which direction you connect the leads. There is no + / - associated with resistance.

11. Measuring Current (Ammeter)DC
ammeter
AC RMS
ammeter + + + ̴
VΩ com A - -
Measuring Current. (Another Yellow measurement card) is a common color for handheld electrical measurement equipment, because it can be seen. This card represents a Digital Voltmeter (DVM). When you plug in the cables as shown, you can measure current The DVM has a dial (not shown) that dials between measuring DC and AC current. When measuring AC current, the value shown will be RMS (root mean square). The ammeter must be placed ‘in line’ with the current. Basically, you disconnect the circuit where you want to measure the current, plug the ammeter in so the negative lead connects to the ‘tail’ of the current to be measured, and plug the + lead in where you would measure the ‘head’ of the current. Note that it matters which side is + and which is -. If you reverse the leads, the current you measure will also be reversed (inverted or ‘minus-ed’). I I - DC AC
RMS

12. Circuit Diagram
Picture From: Wikipedia

13. Series & Parallel

14. Series: CURRENT is the same

15. Parallel: VOLTAGE is the same

17. Wheatstone Bridge
Tune Rv until V= 0
Ru = (R2/R1) Rv V

18. Series / Parallel Battery Charging

26. Nodes, Paths, Loops

27. Conclusion: Circuit Representation
Voltage, Current, Resistance
Variable Resistors / Resistive Sensors
Measuring V,I,R
Series & Parallel elements
Node, Path, loop

28. Introduction to Electrical & Computer Engineering Circuit Representation
Dr. Cynthia Furse
University of Utah
Peekaboo Slot Canyon
Near Kanab, Utah