Digital Design Activities: Parallel and Series Circuits

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. He presented a slightly more complex equation than the one above (see History section below) to explain his experimental results. The equation below is the modern form of Ohm's law. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

$I = \frac{V}{R},$

where

I

is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units ofvolts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.

In physics, the term Ohm's law is also used to refer to various generalizations of the law originally formulated by Ohm. The simplest example of this is:

$\mathbf{J} = \sigma \mathbf{E},$

where J is the current density at a given location in a resistive material, E is the electric field at that location, and σ is a material dependent parameter called the conductivity. This reformulation of Ohm's law is due to Gustav Kirchhoff.

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A parallel circuit has more than one resistor (anything that uses electricity to do work) and gets its name from having multiple (parallel) paths to move along . Charges can move through any of several paths. If one of the items in the circuit is broken then no charge will move through that path, but other paths will continue to have charges flow through them. Parallel circuits are found in most household electrical wiring. This is done so that lights don't stop working just because you turned your TV off.

The following rules apply to a parallel circuit:

The potential drops of each branch equals the potential rise of the source.
The total current is equal to the sum of the currents in the branches.

The inverse of the total resistance of the circuit (also called effective resistance) is equal to the sum of the inverses of the individual resistances.

One important thing to notice from this last equation is that the more branches you add to a parallel circuit (the more things you plug in) the lower the total resistance becomes. Remember that as the total resistance decreases, the total current increases. So, the more things you plug in, the more current has to flow through the wiring in the wall. That's why plugging too many things in to one electrical outlet can create a real fire hazard.

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A series circuit has more than one resistor (anything that uses electricity to do work) and gets its name from only having one path for the charges to move along. Charges must move in "series" first going to one resistor then the next. If one of the items in the circuit is broken then no charge will move through the circuit because there is only one path. There is no alternative route. Old style electric holiday lights were often wired in series. If one bulb burned out, the whole string of lights went off.

The following rules apply to a series circuit:

The sum of the potential drops equals the potential rise of the source.
The current is the same everywhere in the series circuit.
The total resistance of the circuit (also called effective resistance) is equal to the sum of the individual resistances.

Schematic Symbols

A schematic, or schematic diagram, is a representation of the elements of a system using abstract, graphic symbols rather than realistic pictures. A schematic usually omits all details that are not relevant to the information the schematic is intended to convey, and may add unrealistic elements that aid comprehension. For example, a subway map intended for riders may represent a subway station with a dot; the dot doesn't resemble the actual station at all but gives the viewer information without unnecessary visual clutter. A schematic diagram of a chemical process uses symbols to represent the vessels, piping, valves, pumps, and other equipment of the system, emphasizing their interconnection paths and suppressing physical details. In an electronic circuit diagram, the layout of the symbols may not resemble the layout in the physical circuit. In the schematic diagram, the symbolic elements are arranged to be more easily interpreted by the viewer.

Symbol

Component name

Meaning

Wire Symbols

Electrical Wire

Conductor of electrical current

Connected Wires

Connected crossing

Not Connected Wires

Wires are not connected

Switch Symbols and Relay Symbols

SPST Toggle Switch

Disconnects current when open

SPDT Toggle Switch

Selects between two connections

Pushbutton Switch (N.O)

Momentary switch - normally open

Pushbutton Switch (N.C)

Momentary switch - normally closed

DIP Switch

DIP switch is used for onboard configuration

SPST Relay

Relay open / close connection by an electromagnet

SPDT Relay

Jumper

Close connection by jumper insertion on pins.

Solder Bridge

Solder to close connection

Ground Symbols

Earth Ground

Used for zero potential reference and electrical shock protection.

Chassis Ground

Connected to the chassis of the circuit

Digital / Common Ground

Resistor Symbols

Resistor (IEEE)

Resistor reduces the current flow.

Resistor (IEC)

Potentiometer (IEEE)

Adjustable resistor - has 3 terminals.

Potentiometer (IEC)

Variable Resistor / Rheostat (IEEE)

Adjustable resistor - has 2 terminals.

Variable Resistor / Rheostat (IEC)

Trimmer Resistor

Preset resistor

Thermistor

Thermal resistor - change resistance when temperature changes

Photoresistor / Light dependent resistor (LDR)

Photo-resistor - change resistance with light intensity change

Capacitor Symbols

Capacitor

Capacitor is used to store electric charge. It acts as short circuit with AC and open circuit with DC.

Capacitor

Polarized Capacitor

Electrolytic capacitor

Polarized Capacitor

Electrolytic capacitor

Variable Capacitor

Adjustable capacitance

Inductor / Coil Symbols

Inductor

Coil / solenoid that generates magnetic field

Iron Core Inductor

Includes iron

Variable Inductor

Power Supply Symbols

Voltage Source

Generates constant voltage

Current Source

Generates constant current.

AC Voltage Source

AC voltage source

Generator

Electrical voltage is generated by mechanical rotation of the generator

Battery Cell

Generates constant voltage

Battery

Generates constant voltage

Controlled Voltage Source

Generates voltage as a function of voltage or current of other circuit element.

Controlled Current Source

Generates current as a function of voltage or current of other circuit element.

Meter Symbols

Voltmeter

Measures voltage. Has very high resistance. Connected in parallel.

Ammeter

Measures electric current. Has near zero resistance. Connected serially.

Ohmmeter

Measures resistance

Wattmeter

Measures electric power

Lamp / Light Bulb Symbols

Lamp / light bulb

Generates light when current flows through

Lamp / light bulb

Diode / LED Symbols

Diode

Diode allows current flow in one direction only (left to right).

Zener Diode

Allows current flow in one direction, but also can flow in the reverse direction when above breakdown voltage

Schottky Diode

Schottky diode is a diode with low voltage drop

Varactor / Varicap Diode

Variable capacitance diode

Tunnel Diode

Light Emitting Diode (LED)

LED emits light when current flows through

Photodiode

Photodiode allows current flow when exposed to light

Transistor Symbols

NPN Bipolar Transistor

Allows current flow when high potential at base (middle)

PNP Bipolar Transistor

Allows current flow when low potential at base (middle)

Darlington Transistor

Made from 2 bipolar transistors. Has total gain of the product of each gain.

JFET-N Transistor

N-channel field effect transistor

JFET-P Transistor

P-channel field effect transistor

NMOS Transistor

N-channel MOSFET transistor

PMOS Transistor

P-channel MOSFET transistor

Misc. Symbols

Motor

Electric motor

Transformer

Change AC voltage from high to low or low to high.

Electric bell

Rings when activated

Buzzer

Produce buzzing sound

Fuse

The fuse disconnects when current above threshold. Used to protect circuit from high currents.

Fuse

Bus

Contains several wires. Usually for data / address.

Bus

Optocoupler / Opto-isolator

Optocoupler isolates connection to other board

Loudspeaker

Converts electrical signal to sound waves

Microphone

Converts sound waves to electrical signal

Operational Amplifier

Amplify input signal

Schmitt Trigger

Operates with hysteresis to reduce noise.

Analog-to-digital converter (ADC)

Converts analog signal to digital numbers

Digital-to-Analog converter (DAC)

Converts digital numbers to analog signal

Crystal Oscillator

Used to generate precise frequency clock signal

Antenna Symbols

Antenna / aerial

Transmits & receives radio waves

Antenna / aerial

Dipole Antenna

Two wires simple antenna

Logic Gates Symbols
	NOT Gate (Inverter)	Outputs 1 when input is 0
	AND Gate	Outputs 1 when both inputs are 1.
	NAND Gate	Outputs 0 when both inputs are 1. (NOT + AND)
	OR Gate	Outputs 1 when any input is 1.
	NOR Gate	Outputs 0 when any input is 1. (NOT + OR)
	XOR Gate	Outputs 1 when inputs are different. (Exclusive OR)
	D Flip-Flop	Stores one bit of data
	Multiplexer / Mux 2 to 1	Connects the output to selected input line.
	Multiplexer / Mux 4 to 1	Connects the output to selected input line.
	Demultiplexer / Demux 1 to 4	Connects selected output to the input line.

Color Coding..

RESISTOR..

The electronic color code is used to indicate the values or ratings of electronic components, very commonly for resistors, but also for capacitors, inductors, and others. A separate code, the 25-pair color code, is used to identify wires in some telecommunications cables.

The electronic color code was developed in the early 1920s by the Radio Manufacturers Association (now part of Electronic Industries Alliance (EIA)), and was published as EIA-RS-279. The current international standard is IEC 60062.

To distinguish left from right there is a gap between the C and D bands.

band A is first significant figure of component value (left side)
band B is the second significant figure (Some precision resistors have a third significant figure, and thus five bands.)
band C is the decimal multiplier
band D if present, indicates tolerance of value in percent (no band means 20%)

For example, a resistor with bands of yellow, violet, red, and gold will have first digit 4 (yellow in table below), second digit 7 (violet), followed by 2 (red) zeros: 4,700 ohms. Gold signifies that the tolerance is ±5%, so the real resistance could lie anywhere between 4,465 and 4,935 ohms.

Resistors manufactured for military use may also include a fifth band which indicates component failure rate (reliability); refer to MIL-HDBK-199 for further details.

Tight tolerance resistors may have three bands for significant figures rather than two, or an additional band indicating temperature coefficient, in units of ppm/K.

All coded components will have at least two value bands and a multiplier; other bands are optional.

The standard color code per EN 60062:2005 is as follows:

Color	Significant figures	Multiplier	Tolerance		Temp. Coefficient (ppm/K)
Black	0	×10⁰	–		250	U
Brown	1	×10¹	±1%	F	100	S
Red	2	×10²	±2%	G	50	R
Orange	3	×10³	–		15	P
Yellow	4	×10⁴	(±5%)	–	25	Q
Green	5	×10⁵	±0.5%	D	20	Z
Blue	6	×10⁶	±0.25%	C	10	Z
Violet	7	×10⁷	±0.1%	B	5	M
Gray	8	×10⁸	±0.05% (±10%)	A	1	K
White	9	×10⁹	–		–
Gold	–	×10^-1	±5%	J	–
Silver	–	×10^-2	±10%	K	–
None	–	–	±20%	M	–

Any temperature coefficent not assigned its own letter shall be marked "Z", and the coefficient found in other documentation. For more information, see EN 60062. Yellow and Gray are used in high-voltage resistors to avoid metal particles in the lacquer.^[3]

Resistors use preferred numbers for their specific values, which are determined by their tolerance. These values repeat for every decade of magnitude: 6.8, 68, 680, and so forth. In the E24 series the values are related by the 24th root of 10, while E12 series are related by the 12th root of 10, and E6 series by the 6th root of 10. The tolerance of device values is arranged so that every value corresponds to a preferred number, within the required tolerance.

Zero ohm resistors are made as lengths of wire wrapped in a resistor-shaped body which can be substituted for another resistor value in automatic insertion equipment. They are marked with a single black band.

The 'body-end-dot' or 'body-tip-spot' system was used for radial-lead (and other cylindrical) composition resistors sometimes still found in very old equipment; the first band was given by the body color, the second band by the color of the end of the resistor, and the multiplier by a dot or band around the middle of the resistor. The other end of the resistor was colored gold or silver to give the tolerance, otherwise it was 20%.

Capacitor color-coding

Capacitors may be marked with 4 or more colored bands or dots. The colors encode the first and second most significant digits of the value, and the third color the decimal multiplier in picofarads. Additional bands have meanings which may vary from one type to another. Low-tolerance capacitors may begin with the first 3 (rather than 2) digits of the value. It is usually, but not always, possible to work out what scheme is used by the particular colors used. Cylindrical capacitors marked with bands may look like resistors .

	Significant digits	Multiplier	Capacitance tolerance	Characteristic	DC working voltage	Operating temperature	EIA/vibration
Black	0	1	±20%	—	—	−55 °C to +70 °C	10 to 55 Hz
Brown	1	10	±1%	B	100	—	—
Red	2	100	±2%	C	—	−55 °C to +85 °C	—
Orange	3	1000	—	D	300	—	—
Yellow	4	10000	—	E	—	−55 °C to +125 °C	10 to 2000 Hz
Green	5	100000	±0.5%	F	500	—	—
Blue	6	1000000	—	—	—	−55 °C to +150 °C	—
Violet	7	10000000	—	—	—	—	—
Grey	8	—	—	—	—	—	—
White	9	—	—	—	—	—	EIA
Gold	—	—	±5%*	—	1000	—	—
Silver	—	—	±10%	—	—	—	—

*or ±0.5 pF, whichever is greater.

Extra bands on ceramic capacitors will identify the voltage rating class and temperature coefficient characteristics.A broad black band was applied to some tubular paper capacitors to indicate the end that had the outer electrode; this allowed this end to be connected to chassis ground to provide some shielding against hum and noise pickup.

Polyester film and "gum drop" tantalum electrolytic capacitors are also color-coded to give the value, working voltage and tolerance.

APRIL 25, 2014

2. GREEN GREEN RED GOLD

3. ORANGE GREEN BLUE SILVER

APRIL 28, 2014
LOGIC GATES TRUTH TABLES

Digital systems are said to be constructed by using logic gates. These gates are the AND, OR, NOT, NAND, NOR, EXOR and EXNOR gates. The basic operations are described below with the aid of truth tables.

AND gate

The AND gate is an electronic circuit that gives a high output (1) only if all its inputs are high. A dot (.) is used to show the AND operation i.e. A.B. Bear in mind that this dot is sometimes omitted i.e. AB
OR gate

The OR gate is an electronic circuit that gives a high output (1) if one or more of its inputs are high. A plus (+) is used to show the OR operation.

NOT gate

 

The NOT gate is an electronic circuit that produces an inverted version of the input at its output. It is also known as an inverter. If the input variable is A, the inverted output is known as NOT A. This is also shown as A', or A with a bar over the top, as shown at the outputs. The diagrams below show two ways that the NAND logic gate can be configured to produce a NOT gate. It can also be done using NOR logic gates in the same way.

NAND gate

This is a NOT-AND gate which is equal to an AND gate followed by a NOT gate. The outputs of all NAND gates are high if any of the inputs are low. The symbol is an AND gate with a small circle on the output. The small circle represents inversion.
NOR gate

   

This is a NOT-OR gate which is equal to an OR gate followed by a NOT gate. The outputs of all NOR gates are low if any of the inputs are high. The symbol is an OR gate with a small circle on the output. The small circle represents inversion.

EXOR gate

  

The 'Exclusive-OR' gate is a circuit which will give a high output if either, but not both, of its two inputs are high. An encircled plus sign (

) is used to show the EOR operation.

EXNOR gate

  

The 'Exclusive-NOR' gate circuit does the opposite to the EOR gate. It will give a low output if either, but not both, of its two inputs are high. The symbol is an EXOR gate with a small circle on the output. The small circle represents inversion.

The NAND and NOR gates are called universal functions since with either one the AND and OR functions and NOT can be generated.
Note:
A function in sum of products form can be implemented using NAND gates by replacing all AND and OR gates by NAND gates.

A function in product of sums form can be implemented using NOR gates by replacing all AND and OR gates by NOR gates.

74 Series