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Module 3Licence Category B1, B2 and B3

Electrical Fundamentals3.7 Resistance/Resistor

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7-2Module 3.7 Resistance/Resistor Issue 2 – January 2019

Module 3.7 Resistance/ResistorCertification statementThese Study Notes comply with the syllabus of EASA Regulation (EU) No. 1321/2014 Annex III (Part-66) Appendix

I, and the associated Knowledge Levels as specified below:

Objective Part-66 Reference

Knowledge Levels

A B1 B2 B3Resistance/Resistor 3.7 - 2 2 1

(a)Resistance and affecting factors;Specific resistance;Resistor colour code, values and tolerances, preferred values, wattage ratings;Resistors in series and parallelCalculation of total resistance using series, parallel and series-parallel combinations;Operation and use of potentiometers and Rheostats;Operation of Wheatstone Bridge.

(b) - 1 1 -Positive and negative

Objective Part-66 Reference

Knowledge Levels

A B1 B2 B3temperature coefficient conductance;Fixed resistors, stability, tolerance and limitations, methods of construction;Variable resistors, thermistors, voltage dependent resistors;Construction of potentiometers and rheostats;Construction of Wheatstone Bridge.



Module 3.7 Resistance/ResistorTable of Contents

(a)_____________________________________________6Resistivity_____________________________________6Electrical resistance_____________________________8Factors that affect resistance______________________8Resistor definition and symbol____________________12Standard colour code systems____________________12SMD resistors_________________________________16Resistors in series and parallel____________________18Parallel resistance______________________________22Types of resistors______________________________32Potentiometers and rheostats_____________________34Wheatstone bridge_____________________________42

(b)____________________________________________44Conductance__________________________________44Electrical resistor schematic representations_________44LDRs and thermistors___________________________44Resistor characteristics__________________________46Resistor materials______________________________48Resistor wattage rating__________________________52Other properties of resistors______________________54Thermistors___________________________________56Voltage dependant resistors (VDR)________________58Construction of potentiometers and rheostats________60Construction of a Wheatstone bridge_______________62



Module 3.7 Resistance/Resistor



Intentionally Blank

Module 3.7 Resistance/Resistor(a) ResistivityElectrical resistivity (also known as specific electrical resistance) is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electrical charge. The SI unit of electrical resistivity is the ohm metre.

It differs from resistance, in that it depends only on the material, and is a property of the material, and is independent of the dimensions of the conductor.

The electrical resistivity ρ (rho) of a material is given by

ρ = RA𝓁Where:

ρ is the static resistivity (measured in ohm metres, Ω-m);R is the electrical resistance of a uniform specimen of the material (measured in ohms, Ω);𝓁 is the length of the piece of material (measured in metres, m);A is the cross-sectional area of the specimen (measured in square metres, m²).

The unit of resistivity is thus the ohm-meter; values may be obtained from tables where they are usually quoted at 0°C. The resistivities of some of the more common materials in electrical use are shown in the table below.

Resistivity is temperature dependent, with most materials increasing in resistivity as temperature increases. This is called a positive temperature coefficient. Some materials, including all semiconductors, have a negative temperature coefficient. Carbon is a semiconductor material.

The formula quoted for resistivity is usually transposed as follows:

R = ρ 𝓁AThis then provides the resistance of a conductor, given its resistivity, length and cross-sectional area. These are the factors which affect resistance. More discussion on these factors next.






Dimensions of a conductor

MaterialResistivity

at 0°C x 10-8 ohm-metre

Resistivity relative to

copper

Temperature coefficientx 10-4 per °C

Use

Silver 1.51 0.95 41

Good conductors

Copper 1.59 1.00 43

Gold 2.04 1.28 40

Aluminium 2.45 1.54 45

Platinum 9.81 6.17 39.2 Used as conductors because of their other properties

Iron 8.90 5.60 65

Hard steel 46 28.9 16

Mercury 94 59.2 9

Manganin 41 26.1 0.1 Stable resistors (low temperature coefficient)

Constantan

49 30.8 0.4

Nickrome 110 69 1.5

Carbon 7,000 4,425 Negative Very low cost


Resistor definition and symbolA resistor is a passive electrical component with the primary function to limit the flow of electric current.

The international IEC symbol is a rectangular shape. In the USA the ANSI standard is very common, this is a zigzag line (shown on the right).

Standard colour code systems

Band resistorsIn the standard four band resistors, the first two bands indicate the two most significant digits of the resistor’s value. The third band is a weight value, which multiplies the two significant digits by a power of ten.

The final band indicates the tolerance of the resistor. The tolerance explains how much more or less the actual resistance of the resistor can be compared to what its nominal value is. No resistor is made to perfection, and different manufacturing processes will result in better or worse tolerances. For example, a 1 kΩ resistor with 5% tolerance could actually be anywhere between 0.95 kΩ and 1.05 kΩ.

How do you tell which band is first and last? The last, tolerance band is often clearly separated from the value bands, and usually, it’ll either be silver or gold.

Five and six band resistorsFive band resistors have a third significant digit band between the first two bands and the multiplier band. Five band resistors also have a wider range of tolerances available.

Six band resistors are basically five band resistors with an additional band at the end that indicates the temperature coefficient. This indicates the expected change in resistor value as the temperature changes in degrees Celsius. Generally, these temperature coefficient values are extremely small, in the ppm range.

Resistor colour bandsWhen decoding the resistor colour bands, consult a resistor colour code table like the one below. For the first two bands, find that colour’s corresponding digit value. The 4.7 kΩ resistor shown here has colour bands of yellow and violet to begin - which have digit values of 4 and 7 (47). The third band of the 4.7 kΩ is red, which indicates that the 47 should be multiplied by 102 (or 100); 47 times 100 is 4,700.

If you’re trying to commit the colour band code to memory, a mnemonic device might help. There are a handful of (sometimes unsavoury) mnemonics out there to help remember the resistor colour code.

Or, if you remember ‘ROY G. BIV’, subtract the indigo (poor indigo, no one remembers indigo), and add black and brown to the front and grey and white to the back of the classic rainbow colour-order.






Resistor colour code mnemonic

4.7kΩ resistor with four colour bandsAssorted carbon resistors

Module 3.7 Resistance/ResistorCombined 4-band and 5-band colour chartThe same colour chart can be used to determine the value of both 4-band and 5-band resistors. On the 4-band resistor, the ‘3rd-band’ column of the chart is ignored.






Assorted carbon resistors

Colour code charts for 4-, 5- and 6-band resistors


Resistors in series and parallel

Series resistanceReferring to the diagram below, the current in a series circuit must flow through each lamp to complete the electrical path in the circuit. Each additional lamp offers added resistance. In a series circuit,

the total circuit resistance (RT) is equal tothe sum of the individual resistances.

As an equation:RT = R1 + R2 + R3 + … RnNote: The subscript ‘n’ denotes any number of additional

resistances that might be in the equation.



Module 3.7 Resistance/ResistorExample: In the figure below left a series circuit consisting of three resistors: one of 10 ohms, one of 15 ohms, and one of 30 ohms, is shown. A voltage source provides 110 volts. What is the total resistance?

Given: R1 = 10 ohmsR2 = 15 ohmsR3 = 30 ohmsSolution: RT = R1 + R2 + R3RT = 10 ohms + 15 ohms + 30 ohms RT = 55 ohmsIn some circuit applications, the total resistance is known and the value of one of the circuit resistors has to be determined. The equation RT = R1 + R2 + R3 can be transposed to solve for the value of the unknown resistance.

Example: In the figure below right the total resistance of a circuit containing three resistors is 40 ohms.

Two of the circuit resistors are 10 ohms each. Calculate the value of the third resistor (R3).

Given:R1 = 40 ohmsR2 = 10 ohmsR3 = 10 ohmsSolution:RT = R1 + R2 + R3

(Subtract R1 + R2 from both sides of the equation)RT – R1 – R2 = R3R3 = RT – R1 – R2R3 = 40 ohms – 10 ohms – 10 ohmsR3 = 40 ohms – 20 ohmsR3 = 20 ohms



Comparison of basic and series circuits.




Solving for total resistance in a series circuit. Calculating the value of one resistance in a series circuit.


Parallel resistanceIn the example diagram below there are two resistors connected in parallel across a 5-volt battery. Each has a resistance value of 10 ohms. A complete circuit consisting of two parallel paths is formed and current flows as shown.

Computing the individual currents shows that there is one-half of an ampere of current through each resistance. The total current flowing from the battery to the junction of the resistors, and returning from the resistors to the battery, is equal to 1 ampere.

The total resistance of the circuit can be calculated by using the values of total voltage (VT) and total current (IT).

Note: From this point on the abbreviations and symbology for electrical quantities will be used in example problems.

Given: VT = 5VIT = 1A

Solution:

R = VIRT

= VTIT

RT

= 5V1ART

= 5ΩThis computation shows the total resistance to be 5 ohms; one-half the value of either of the two resistors.

Since the total resistance of a parallel circuit is smaller than any of the individual resistors, the total resistance of a parallel circuit is not the sum of the individual resistor values as was the case in a series circuit. The total resistance of resistors in parallel is also referred to as equivalent resistance (Req). The terms total resistance and equivalent resistance are used interchangeably.






Two equal resistors connected in parallel.

Module 3.7 Resistance/ResistorThere are several methods used to determine the equivalent resistance of parallel circuits. The best method for a given circuit depends on the number and value of the resistors. For the circuit described above, where all resistors have the same value, the following simple equation is used:R

eq = RNReq = equivalent parallel resistanceR = ohmic value of one resistorN = number of resistors

This equation is valid for any number of parallel resistors of equal value.

Example: Four 40-ohm resistors are connected in parallel. What is their equivalent resistance?

Given: R1 + R2 + R3 + R4R1 + 40ΩSolution: R

eq = RNReq = 40Ω4

Req = 10Ω

Example: The diagram below shows two resistors of unequal value in parallel. Since the total current is shown, the equivalent resistance can be calculated.

Given: Vs = 30VIT = 15ASolution:

Req = V

SIT

Req = 30V15AReq = 2Ω

The equivalent resistance of the circuit shown in the diagram below is smaller than either of the two resistors (R1, R2). An important point to remember is that the equivalent resistance of a parallel circuit is always less than the resistance of any branch.



Module 3.7 Resistance/ResistorEquivalent resistance can be found if you know the individual resistance values and the source voltage. By calculating each branch current, adding the branch currents to calculate total current, and dividing the source voltage by the total current, the total can be found. This method, while effective, is somewhat lengthy. A quicker method of finding equivalent resistance is to use the general formula for resistors in parallel: 1 = 1 + 1 + 1 + … 1R

eqR1

R2

R3

Rn

If you apply the general formula to the circuit shown in the diagram below you will get the same value for equivalent resistance (2Ω) as was obtained in the previous calculation that used source voltage and total current.

Given: R1 = 3 ΩR2 = 6 ΩSolution: 1 = 1 + 1R

eqR1

R2

1 = 1 + 1Req

3 Ω 6 Ω

Convert the fractions to a common denominator.1 = 2 + 1Req

6 Ω 6 Ω1 = 3Req

6 Ω1 = 1Req

2 ΩSince both sides are reciprocals (divided into one), disregard the reciprocal function.Req = 2 ΩThe formula you were given for equal resistors in parallel

( Req = R is a simplification of

the general formula for resistors in parallel

)N1 = 1 + 1 + 1 + … 1Req

R1

R2

R3

Rn



Example circuit with unequal parallel resistors.

Module 3.7 Resistance/ResistorThere are other simplifications of the general formula for resistors in parallel which can be used to calculate the total or equivalent resistance in a parallel circuit.






Example circuit with unequal parallel resistors.

Module 3.7 Resistance/ResistorReciprocal method - This method is based upon taking the reciprocal of each side of the equation. This presents the general formula for resistors in parallel as:

Req = 11 + 1 + ⋯ 1R

1R2

Rn

This formula is used to solve for the equivalent resistance of a number of unequal parallel resistors. You must find the lowest common denominator in solving these problems.

Example: Three resistors are connected in parallel as shown in the diagram below. The resistor values are: R1 = 20 ohms, R2 = 30 ohms, R3 = 40 ohms. What is the equivalent resistance? (Use the reciprocal method.)

Given: R1 = 20 ΩR2 = 30 ΩR3 = 40 Ω

Solution:

Req = 11 + 1 + 1R

1R2

R3

Req = 11 + 1 + 120 Ω 30 Ω 40 ΩReq = 16 + 4 + 3120 Ω 120 Ω 120 ΩReq = 113 Ω120Req = 120 Ω13Req = 9.23 Ω






Example parallel circuit with unequal branch resistors


Types of resistors

Fixed resistors – As the name implies, these resistors have a fixed resistance and tolerance regardless of any changes in temperature, light, etc.

Variable resistors – These parts have a modifiable resistance. The potentiometer is a great example, which has a dial that can be turned to ramp up or down the resistance. Other variable resistors include the trimpot and rheostat.






Variable resistors

Fixed resistors

Module 3.7 Resistance/ResistorPotentiometer as an electronic componentA potentiometer is a potential divider, a three-terminal resistor where the position of the sliding connection is user adjustable via a knob or slider. Potentiometers are sometimes provided with one or more switches mounted on the same shaft. For instance, when attached to volume control, the knob can also function as an on/off switch at the lowest volume.

Ordinarily, potentiometers are rarely used to directly control anything of significant power (more than a watt). Instead, they are used to adjust the level of analogue signals (e.g. volume controls on audio equipment), and as control inputs for electronic circuits. For example, a light dimmer uses a potentiometer to control the switching of a triac and so indirectly control the brightness of lamps.

RheostatsA rheostat is a two-terminal variable resistor. Often these are designed to handle much higher voltage and current. Typically these are constructed as a resistive wire wrapped to form a toroid coil with the wiper moving over the upper surface of the toroid, sliding from one turn of the wire to the next. Sometimes a rheostat is made from resistance wire wound on a heat-resisting cylinder with the slider made from a number of metal fingers that grip lightly onto a small portion of the turns of resistance wire. The ‘fingers’ can be moved along the coil of resistance wire by a sliding knob thus changing the ‘tapping’ point. They are usually used as variable resistors rather than variable potential dividers.

Any three-terminal potentiometer can be used as a two-terminal variable resistor, by not connecting to the 3rd terminal. It is common practice to connect the wiper terminal to the unused end of the resistance track to reduce the amount of resistance variation caused by dirt on the track.

Applications of potentiometers and rheostatsPotentiometers are widely used as user controls and may control a very wide variety of equipment functions.

The widespread use of pots in consumer electronics has declined in the 1990s, with digital controls now more common. However, they remain in use in many applications. Two of the most common applications are as volume controls and as position sensors.






Various types of potentiometers

Linear potentiometer

Rotary potentiometer

Rotary potentiometer

Interior components of a rotary potentiometer

Trimmer potentiometer

or

symbolsymbols

PotentiometerRheostat

Module 3.7 Resistance/ResistorAudio controlSliding potentiometers (‘faders’)

One of the most common uses for modern low-power potentiometers is as audio control devices. Both sliding pots (also known as faders) and rotary potentiometers (commonly called knobs) are regularly used to adjust loudness, frequency attenuation and other characteristics of audio signals.

The ‘log pot’ is used as the volume control in audio amplifiers, where it is also called an ‘audio taper pot’ because the amplitude response of the human ear is also logarithmic. It ensures that on a volume control marked 0 to 10, for example, a setting of 5 sounds half as loud as a setting of 10. There is also an anti-log pot or reverse audio taper which is simply the reverse of a log pot. It is almost always used in a ganged configuration with a log pot, for instance, in audio balance control.

Potentiometers used in combination with filter networks act as tone controls.

TransducersPotentiometers are also very widely used as a part of position transducers because of the simplicity of construction and because they can give a large output signal.






Sliding potentiometers

Module 3.7 Resistance/ResistorTheory of operationA potentiometer with a resistive load, showing equivalent fixed resistors for clarity, is shown in the diagram below.

The potentiometer can be used as a potential divider (or voltage divider) to obtain a manually adjustable output voltage at the slider (wiper) from a fixed input voltage applied across the two ends of the pot. This is the most common use of pots.

One of the advantages of the potential divider compared to a variable resistor in series with the source is that, while variable resistors have a maximum resistance where some current will always flow, dividers are able to vary the output voltage from maximum (VS) to ground (zero volts) as the wiper moves from one end of the pot to the other. There is, however, always a small amount of contact resistance.

In addition, the load resistance is often not known and therefore simply placing a variable resistor in series with the load could have a negligible effect or an excessive effect, depending on the load.






The potentiometer and its equivalent circuit as a voltage divider


Wheatstone bridge

Operation of the Wheatstone bridgeA Wheatstone bridge is a measuring instrument invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. It is used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. Its operation is similar to the original potentiometer except that in potentiometer circuits the meter used is a sensitive galvanometer.

The basic bridge circuitThe fundamental concept of the Wheatstone Bridge is two voltage dividers, both fed by the same input, as shown to the right. The circuit output is taken from both voltage divider outputs, as shown here.

In its classic form, a galvanometer (a very sensitive DC current meter) is connected between the output terminals and is used to monitor the current flowing from one voltage divider to the other. If the two voltage dividers have exactly the same ratio (R1/R2 = R3/R4), then the bridge is said to be balanced and no current flows in either direction through the galvanometer. If one of the resistors changes, even a little bit in value, the bridge will become unbalanced and current will flow through the galvanometer. Thus, the galvanometer becomes a very sensitive indicator of the balance condition.

Using the Wheatstone bridgeIn its basic application, a DC voltage (V) is applied to the Wheatstone Bridge, and a galvanometer (G) is used to monitor the balance condition.

The values of R1 and R3 are precisely known but do not have to be identical. R2 is a calibrated variable resistance, whose current value may be read from a dial or scale.

An unknown resistor, RX, is connected as the fourth side of the circuit, and power is applied. R3 is adjusted until the galvanometer, G reads zero current. At this point, RX = R2 × R3/R1. This circuit is most sensitive when all four resistors have similar resistance values. However, the circuit works quite well in any event. If R2 can be varied over a 10:1 resistance range and R1 is of a similar value, we can switch decade values of R3 into and out of the circuit according to the range of value we expect from RX. Using this method, we can accurately measure any value of RX by moving one multiple-position switch and adjusting one precision potentiometer.

Applications of the Wheatstone bridgeOne very common application in the industry today is to monitor sensor devices such as strain gauges. Such devices change their internal resistance according to the specific level of strain (or pressure, temperature, etc.), and serve as the unknown resistor RX. However, instead of trying to constantly adjust R2 to balance the circuit, the galvanometer is replaced by a circuit that can be calibrated to record the degree of imbalance in the bridge as the value of strain or other condition applied to the sensor.






The basic Wheatstone bridge circuit The practical Wheatstone bridge




Construction of a wheatstone bridge using 3 carbon resistors and a rheostat (the unknown)

A wheatstone bridge test board

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