rg mod3 3.7 resistance and resistors

Resistance is an electrical property of a conductor. As explained previously, for a given current, a higher resistance requires

a higher voltage to be applied across the conductor.

The numerical value of a conductor's resistance depends on several factors, including

the material from which it is made, its shape, and its size.

Factors affecting the electrical resistance of a particular object, i.e., an electrical component, are determined by:

• The length of the object.

• The cross-sectional area of the object.

• The material from which the object is made.

Resistance increases in

direct proportion to the length of a resistor; if the material is doubled in length, then the resistance is also doubled.

Resistance increases in inverse proportion to

the cross-sectional area of a resistor; if the resistor is doubled in cross-sectional area, then the resistance is halved.

All materials oppose the flow of an electric current to some extent. To compare the resistances of various materials, it is important to compare samples with

the same dimensions, for example, all samples can be prepared like this:

• Length: L = 1 m

• Cross-sectional area: q = 1 mm²

• Temperature: 20℃

The resulting measurements of resistance allow a quantitative comparison of the resistance of different materials.

Specific resistance, also known as

resistivity, is an electrical property of a material.

Specific resistance gives a measure of

the resistance of the material

The resistance of a conductor made from the material can then be calculated if

its dimensions are known

The relationship between length, cross-sectional area, and resistance can be expressed mathematically as:

R =inversely proportional to L/A

R= “rho”L/A

Where R is resistance in ohms (Ω), L is the length in metres (m), and A is the cross-sectional area in square metres (m²).

The constant of proportionality in this equation is known as the specific resistance (or resistivity) and is given the symbol ⍴, pronounced ‘rho’. This has units of ohm metres (Ωm).

Ohm metres (Ωm) is the SI unit, but it is common in engineering to also quote figures in

ohm millimetres squared per metre (Ωmm²/m), as this is easier to relate to a standard piece of wire with dimensions of 1 m in length and 1 mm² in cross-sectional area.

To use these alternative units the same formula is applied but the units for the cross-sectional area must now be in mm².

Specific resistance is used to calculate the resistance of conductors

of any size

The formula used taking care to ensure that the units of specific resistance used are compatible with the units of the cross-sectional area being used.

“rho”= RXA/L

Resistors that are designed to provide a constant value of resistance are referred to as

fixed resistors and those which are designed to provide a range of resistance values are referred to as variable resistors.

A wire of a cross-sectional area of 2 mm² is required to connect two components that are separated by a distance of 10 m. What is the resistance of one such length of wire, if it is made from:

• Copper, with a specific resistance of 0.020 Ωmm²/m?

• Iron, with a specific resistance of 0.100 Ωmm²/m?

To solve this problem, for each metal, first, write down the equation in full and then substitute the known values. Since the specific resistance is given in units of Ωmm²/m and the cross-sectional area is in mm², there is no need to convert any of the values to different units.

For the copper wire:

For the iron wire:

At a temperature of 20℃, a copper wire that is 1 m long, with a cross-sectional area of 1 mm², has a resistance of 0.0178 Ω. A copper wire twice that length, with the same cross-sectional area, has double the resistance, i.e., 0.0356 Ω. A wire three times as long has

three times the resistance.

Resistors are designed and manufactured to have a particular value of resistance. This value is indicated on

the body of the resistor using a colour code. it is important that engineers either building or maintaining electrical circuits can read these codes.

depending on the precision to which they are manufactured, the actual value of resistors varies a little. This variation, given as a

percentage, is also included in the colour code on the resistor body and is known as the tolerance.

resistor tolerance then determines the interval between different resistance values available across a range of resistances—otherwise,

resistors labelled as having different values can have the same value.

Resistors are designed to dissipate a maximum amount of power. Beyond this power,

a resistor's temperature becomes too great, with risks including damage to the circuit and fire.

at this point its time to find a resistor colour code value and tolerance for 3min

had enough now?

The tolerance of a resistor is the extent to which it can differ from

the rated value.

standard range and tolerance.

The allocation is done in such a way that the sections overlap one another so that

no waste is produced

Resistors are produced with particular rated values, according to the IEC standard range. Each range has its factor or percentage, which determines

how much bigger a value is than its predecessor, thereby defining the difference between one value and the next.

The electrical energy applied to a resistor is converted completely into heat (dissipated as heat), which increases the temperature of the resistor. The rate at which energy is converted to heat and dissipated by a resistor must be less than

the wattage rating

Overheating the resistor damages the materials from which it is constructed, affecting both

the technological and physical properties

A resistor must be able to release heat into its environment to prevent such damage, e.g., burning or melting. This can be done by

increasing the surface area while maintaining the cross-sectional area of the resistor. In a wire-wound resistor, this can be achieved by using a long wire of a greater diameter, maintaining the same resistance.

The power rating of a resistor is the maximum power (or wattage) that can be dissipated by the resistor without

affecting its function.

For small components, these values range between 50 and 500 mW. Large wire-wound resistors can cope with 100 W and more.

In addition to the rated value of the resistor, the power rating at ambient temperatures of 40℃ (104℉) and 70℃ (158℉) is often stated. Ambient temperatures above the stated value will

invalidate the power rating as the resistor will fail at a lower power due to not being able to dissipate the heat energy at a fast enough rate.

the method of calculation of the total resistance of a group of resistors depends upon

how they are connected

There is a formula for series connections and a different formula for parallel connections. Where groups of resistors are connected in a combination of series and parallel arrangements, each formula must be applied in turn.

If resistors are connected in series, the current must flow through them all in turn, like water running through different sections of the same hose pipe. The current only has one way to go and so has

the same value for each resistor

I(TOTAL) = I1 = I2 = I3

When resistors are connected in series, the values of the resistors can be

combined to give a single value, which in this case is called R_Total.

any number of resistors in series, simply

add the values to calculate the total resistance.

A series connection has three typical features:

• The voltage provided by the battery is divided between the resistors, depending on their resistances.

• The current is the same through all components.

• The individual resistances must be added together to find the total resistance.

A series connection can also be described as a potential divider (or voltage divider). Each resistor has only a part of the total voltage across it. This part of the input voltage V_in can be tapped at a certain point, called the

“pick-up”, to produce a smaller voltage V_out.

Connecting resistors in parallel offer more than one path to the current, so the current

splits up and a smaller current flows through each available path. This effectively increases the conductor cross-section.

Each resistor receives part of the current. With resistors in parallel, the area through which the current can flow increases, which

decreases the resistance.( apply kirchoffs first law and ohms law)

to calculate Rtotal in a parallel circuit

simply add the reciprocals of the individual resistances to find the reciprocal of the total resistance.

A parallel connection has three typical features:

• Voltage is the same across each resistor.

• The total current is the sum of the currents in each branch.

• The total resistance is lower than the lowest individual resistance.

 

A 3 Ωresistor is placed in series with a 4 Ω resistor. What is the effective resistance of this combination?

7 Ω

A circuit contains a series connection of a 3 A circuit contains a series connection of a 3kΩ,1kΩ and 500kΩresistor. What is the effective resistance of this part of the circuit?

4500kΩ

A 3 Ω resistor is placed in parallel with a 4 Ω resistor. What is the effective resistance of this combination?

1.7Ω

Where circuits contain combinations of resistors that are a mixture of series and parallel combinations, each formula must be applied

separately. First calculate the effective resistance of groups of either series or parallel resistors, until the whole problem is reduced to either a series or parallel combination only.

Variable resistors have adjustable

resistance values

A variable resistor is an

electro-mechanical transducer, which normally works by sliding a contact (wiper) over a resistive element

When a variable resistor is used as a potential divider, with three terminals, it is called a

‘potentiometer’

When a variable resistor is used as a potential divider, with two terminals, it functions as a

variable resistance and is called a ‘rheostat’

Variable resistors can be controlled

electronically or mechanically.

Electronically controlled resistors are called

“digital potentiometers”.

In addition to fixed resistors, several variable resistors can be used in electrical and electronic circuits. These range from:

• Mechanically varied resistor

• Positive or negative temperature coefficient resistor

• Voltage dependant resistor

The choice of the variable resistor depends on

the application of the circuit.

Circuits requiring a variation in voltage use

potentiometer

a Potentiometers are sometimes referred to as 'pots', connected as a variable potential divider.

Circuits requiring a variation in the current use

a rheostat

A potentiometer is a three-terminal device, used to control

voltage

A rheostat is a two-terminal device, used to control

current

The difference between the potentiometers and rheostat is much more to do with

how they are connected than with their material construction.

Rheostats compared to Potentiometers are often required to operate at

higher currents and are therefore larger, with a higher power rating, but this is not always the case and the same device is often used for both applications.

To configure as a potentiometer the 3 terminals are connected

terminal 3 is connected to the input voltage, terminal 1 to the zero or ground, and terminal 2 then becomes the variable output voltage.

This provides the full range of potential differences from the input voltage down to zero.

A potentiometer controls voltage. It is a three-terminal device with a sliding or rotating contact (wiper) moving over a resistive element that forms an adjustable voltage divider. They are often used to control voltages such as in

volume controls in audio circuits and brightness in lighting circuits.

Another use for a potentiometer is varying the speed of DC motors. By using a potentiometer, the voltage supplied across the motor can be adjusted, and this voltage adjustment will then

change the speed of the motor

A potential difference is applied between 1 and 3. The position of the wiper determines the

resistance ratio of 1 to 2 and 2 to 3, forming a potential divider and controlling the voltage at 2 (the tap off point)

Pre-set potentiometers are commonly mounted on

printed circuit boards. They have a limited range and are usually set during manufacture or maintenance.

In an electric circuit, it is often desirable to restrict the current, which can either be done by

reducing the voltage or increasing the resistance in the circuit (Ohm’s Law). A rheostat is a device that facilitates this.

To configure as a rheostat, there are two alternative arrangements. Each of these effectively leaves the device with two terminals.

• Option 1: terminal 3 is connected to the input current and terminal 2 provides the output current. Terminal 1 is not connected to the circuit.

• Option 2: terminal 3 is connected to the input current and terminals 1 and 2 are connected to form the output terminal for the current.

A rheostat is a variable resistor that controls the current within a circuit. It is a two-terminal device. In low-power operations,

they are made by using two terminals of a potentiometer: the wiper terminal and one of the other terminals. Higher-power devices typically consist of a wiper moving over copper windings.

Pre-set rheostats are usually mounted on printed circuit boards. They have a limited range and are usually set during

manufacture or maintenance.

A potential difference is applied between 1 and 2; the position of the wiper determines the resistance between 1 and 2, the larger the resistance the

smaller the current.

Metals are conductors. Increasing the temperature of a conductor increases the rate of thermal agitation and, consequently

the rate of collisions. This increases resistivity which, in turn, decreases conductivity.

Conductors whose resistance increases in line with temperature are said to have a

Positive Temperature Coefficient (PTC).

in a resistor The value of the temperature coefficient is the proportion by which the

resistance of a resistor changes

A positive value of temperature coefficient indicates that the

resistance increases with increasing temperature

A negative value of temperature coefficient indicates that the

resistance decreases with increasing temperature.

Proportional change in resistance =

change in temperature x temperature coefficient

The temperature coefficient typically has very small

numerical values. For a carbon film resistor, this can be around 0.0008/K.

The units for temperature coefficient are sometimes expressed as ppm/K, which stands for

parts per million per kelvin, and is the same number multiplied by one million, so this value becomes 800 ppm/K.PTC

For example, a 10 kΩ resistor with a temperature coefficient of +0.0008 /K, subjected to an increase in temperature of 100 degrees above the standard operating temperature (usually 20℃), suffers an increase in resistance by a factor of 0.0008 x 100 = 0.08. So, the resistance increases by

0.08 x 10 000 = 800 Ω, which can cause a significant problem, depending on the tolerances of the circuit and application.

The graph for PTC conductors follows a

linear upward gradient.

semiconductors, whose resistivity decreases as temperature increases, are described as

Negative Temperature Coefficient (NTC) materials; their graph follows a downward curve.

Fixed resistors have a fixed electrical resistance, which is not

adjustable

fixed resistors are the more commonly used resistors and one of the most

common electronic components.

Variable resistors have a resistance value that can be set at different values, or that changes in response to changes in the

environment, such as temperature or light for example.

resistors are constructed in different ways, depending on

the intended use and purpose

The size and shape of the material used affects the resistance value, and different materials of the same size produce

different resistance values.

Resistors are used to contro

voltage or current in a circuit or to detect changes in the environment.

Fixed resistors can have axial leads, surface mount packages, or more customised packages,

depending on their use

Axial lead resistors used to be the most common resistors, but nowadays

Surface Mounted Device (SMD) resistors are the most popular, thanks to their advantages.

A perfect resistor has a constant ohmic resistance under

ll circumstances, independent of frequency, voltage, or temperature. In practice, no resistor is perfect and resistance values vary within defined tolerance limits for each particular application.

The type of resistor and its material composition determine the extent to which external factors affect resistance values. Therefore, the choice of resistor (and material) needs to be based on the

required accuracy, power dissipation, and noise considerations.

The graphic below gives an overview of the most popular, common fixed resistors.

now have a look…….finished?

The carbon film is the most common

axial lead resistor and is used for applications that do not require a very good tolerance or temperature coefficient.

Axial lead refers to

the direction in which the connecting leads enter and leave the resistor body. Many fixed resistors are cylindrical, and the connecting wires are aligned with the central axis of the cylinder as if it were a wheel. and is used for applications that do not require a very good tolerance or temperature coefficient.

the metal film is the general axial lead resistor of choice for

higher-precision applications

Wire wound resistors are typically used for

high-power applications

aluminium housing is often used for power ratings from

1 to 200 W

SMD (surface mounted device) resistors are mostly constructed from

thick or thin film material.

Variable resistors have adjustable resistance values. A variable resistor normally works by

sliding a contact (wiper) over a resistive element, controlled by an external knob or slider.

When a variable resistor is used as a potential divider, with three terminals, it is called a

‘potentiometer’. When it only has two terminals, it functions as a variable resistance and is called a ‘rheostat’. Variable resistors can be controlled electronically or mechanically.

Normally, resistors maintain the same resistance over a

wide range of temperatures.

A change of resistance with temperature can be desirable for certain purposes e.g., for

the Total Air Temperature (TAT) probe (used to measure the air temperature outside an aircraft).

Generally, there are two possible responses to a rise in temperature: the resistance either

increases or decreases.

Depending on these thermal characteristics, there are two thermistor types:

• Positive Temperature Coefficient (PTC) Resistors

• Negative Temperature Coefficient (NTC) Resistors