Introduction to Resistors

OCTOBER 31, 2015 BY ADMINISTRATOR LEAVE A COMMENT

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What is Resistor?

A resistor is a device in which electricity cannot pass through it easily. When certain amount electricity is allowed to pass through a resistor, the electrical energy is changed into another form.The other form of energy is usually light or heat. The working principle of bulb is that electricity is passed through the filament usually tungsten, which is a resistor. The energy is converted to and released as light and heat.

The resistor is an electrical component which creates a resistance in the flow of electric current.

A resistor is a basic electrical component found in almost all electronic circuits and electrical networks. A resistor is two terminal passive electrical component. It is a passive component as it consumes energy from a source (active component).

Although resistors are generally used to reduce the flow of current or lower the levels of voltage in a circuit, they are used in many electronic circuits for many purposes. Some of them are the basic current flow limitation ability, to provide a biasing condition to some of the active elements like transistors or to act as a terminating device in transmission lines.

Practically resistors are discrete components of various forms but are also implemented on integrated circuits.

ResistorSymbols

Generally there are two standards that are used to denote the symbol of a resistor viz.Institute of Electrical and Electronics Engineers (IEEE) and International Electro Technical Commissions (IEC).

The IEEE symbol of resistor is a zigzag line as shown in the below figure.

Resistor IEEE Symbol

The IEC symbol

Resistor IEC Symbol

There are some other symbols of resistors in use , based on the type. Each type has both IEEE symbol and IEC symbol. The types of resistors are potentiometer and variable resistor which is generally known as rheostat.

The IEEE symbol for potentiometer is

Potentiometer IEEE Symbol

The IEC symbol for potentiometer is

Potentiometer IEC Symbol

The IEEE symbol for rheostat is

Rheostat IEEE Symbol

The IEC symbol for rheostat is

Rheostat IEC Symbol

Resistance

The mechanism of energy flow through a conductor can be described as follows: In the presence of an active source, the passive elements like resistors will always absorb energy and the currents through them will always flow from higher potential to lower potential.

If we apply the same potential difference between the ends of two different but geometrically similar conductors like rods of copper and of glass, it results in different currents. This characteristic of the conductor that results in different currents is its electrical resistance.

The definition of resistance can be derived from the Ohm’s law in its Electromagnetic theory form or Continuum form

J = σ E —-1

Here σ is the conductivity of the material i.e. conductor.

E is the electric field developed along the length of conductor due to flow of electrical energy through the conductor.

If ‘V’ is the voltage drop across the conductor and ‘L’ is the physical length of conductor then

E = V/L —-2

The current density J is resulted within the conductor due to the flow of electrical energy through the conductor.

If ‘I’ is the current flowing through the conductor and ‘A’ is the cross sectional area of conductor, then by the definition of current density

J = I/A —-3

Now combining equations 1, 2 and 3

I/A = σ V/L

V = (L/Aσ) I —-4

The term in parenthesis is constant and let us denotes it by ‘R’.

∴V = R I

This is the Ohm’s law form in circuit analysis.

By the definition of Ohm’s law, the current flowing through a conductor is directly proportional to the potential difference applied.

I ∝ V

The proportional constant is called Resistance parameter of the conductor R.

∴I = V/R

R = V/I

The resistance of a conductor, between its two points is determined, by applying a potential difference V between those two points and measuring the current I .

The unit of resistance is Volts per Ampere and is given the name Ohm (Ω).

∴ 1Ω = 1 volt per ampere = 1 V/A.

From earlier calculations

V = (L/Aσ) I

∴ R = L/(A σ) I

σ is the conductivity of the conductor which is the measure of conductor’s ability to conduct electric current.

1/σ is the reciprocal of electrical conductivity called electrical resistivity denoted by the symbol ρ (rho).

Resistivity is the measure of a conductor’s ability to resist the flow of electric current.

∴Resistance of a material ∝ resistivity of the material.

R = ρL/A Ω

Resistance of a conductor can be defined as the conductor’s opposition to the flow of current through it.

Resistance is a property of an object like conductor. Resistivity is a property of a material from which the object is made.

The definition of resistor can be written as

A conductor whose function is to provide a specified resistance in a circuit.

Resistance Measurement

Resistors are main components in electric and electronic circuits as they determine the amount of current that flows in a circuit and also the potential at different points in a circuit. Therefore it is important to make sure that the value of resistance is known for a given resistor which is placed in a circuit.

From Ohm’s law, it is easy to calculate the resistance. Ohm’s law relates the Voltage V, Current in the circuit I and the Resistance of the resistor R.

R = V/I

∴In terms of units, 1 Ohm (Ω) = 1 Volt (V) / 1 Ampere (A).

In other terms, a resistor is said to be having a resistance of 1Ω when 1A of current is passed through it for a supply voltage of 1V.

Ohmmeter is a device designed specifically for this purpose. A resistor is connected across the terminals of ohmmeter and the reading of the ohmmeter is the value of the resistance of that resistor along with the resistance offered by the wires used to connect the resistor to ohmmeter.

Even though the resistance of wire is very small, it can’t be neglected. Hence the values measured using an ohmmeter is not accurate.

The next best way to determine the resistance is to make use of both voltmeter and an ammeter in the circuit.

The set up can be as follows

In this method, the readings both current and voltage are taken using the respective devices. If we consider the resistances of the wire then the circuit will be

Since it is a series loop, current will be same at all the points. Because the voltmeter is used to measure the voltage drop across the unknown resistor, wire resistances doesn’t come into picture.

∴RX = Voltmeter Reading / Ammeter Reading

The above setup is good if internal resistance of the voltmeter is larger compared to the RX.

In case of resistance RX is larger than that of internal resistance of the voltmeter then the following setup can be used.

Another technique is used for the measurement of lower resistances. This is called Four Terminal Sensing or Kelvin Sensing.

To measure the lower resistance (< 100Ω), the Kelvin Sensing is used to eliminate the inappropriate influence of contact resistances and wiring resistances.

This connection method for resistance measurement uses separate pairs of current-carrying and voltage-sensing probes to eliminate the influence of contact and test lead resistances which appear in the precious setup which is also called Two Terminal Sensing.

The four terminal sensing method with internal resistances of wire can be depicted as follows:

The resistance of Rx1 can be calculated as follows

The current which passes through the voltage-sensing path or terminals is very less than the current through the resistor RX1. This implies that the voltage drop across the wire resistances in the voltage-sensing path is very less.

∴ I = IRX1 + IVPath ≈ IRX1

Now the voltage across the resistor RX1 is the value of voltmeter VRX1.

∴ RX1 = VRX1 / IRX1

Resistivity

Often the ability of a material to conduct electricity or the electrical transport property of a material is measured by the conductivity of the material.

Electrical Conductivity of a material is the measure of its ability to conduct current.

Resistivity is the reciprocal of conductivity. Resistivity is the measure of a conductors’ ability to resist the flow of electric current.

Derivation

Assume a material of length ‘ L’ and area of cross section ‘A’ and resistance ‘R’.

Resistance to the of the material is directly proportional to the length ‘L’ and inversely proportional to area of cross section ‘A’.

Thus

R ∞ L ,

R ∞ 1/A ,

Combining above two equations

R ∞ L / A

Assume a constant ‘ρ’to eliminate proportionality

So, R =(ρ ×L) /A.

Hence ρ = (R×A) / L.

Thus from above equation materials with low resistivity allows the movement of electrons while those with high resistivity oppose the flow of electrons.

Elements like copper, aluminum will have low resistivity

Units of resistivity are Ohm-meter (Ω-mt).

In mathematical terms, the definition of resistivity is resistance per unit length per unit cross sectional area of the material.

In electromagnetic theory, the term resistivity can be defined as the magnitude of electric field across the material that results in a certain current density.

ρ = E / J

E is the electrical field and J is the current density.

Resistance Example:

If a rectangular block of iron (with ρ = 9.68 x 10-8Ω.m) of dimensions 1.2cm x 1.2cm x 15cm is applied with a potential difference such that the sides are equipotential, find the resistance.

Solution:

L = 15cm = .15m

A = 1.2cm×1.2cm = 1.44× 10-4 m2

∴R = ρL/A

R = (9.68× 10-8Ω.m ×.15m) / (1.44 × 10-4 m2)

R = 1 × 10-4Ω = 1µΩ

Resistance Units

Resistance R = V/I

This results in the units of resistance as volts per ampere. This combination is given a special name called Ohm named after the physicist Georg Simon Ohm.

∴ 1Ω = 1 volt per ampere

The units of conductance which is reciprocal of resistance is given by 1/Ω and given the name Mho. Mho is Ohm written in reverse. It is given by the symbol ℧. Later this is changed to Siemens (S).

S = Ω-1 = A/V.

The value of Ω can be defined in various forms as shown in the below equation

Where

Ω is the resistance
V is Volts
A is Ampere
Kg is Kilogram
m is meter
s is second
C is Coulomb
J is Joule
S is Siemens
F is farad
W is Watt

Carbon Resistors

Carbon Composition Resistors are commonly used resistors which are manufactured at low cost. This is because of the simpler construction process. They are generally called carbon resistors. The main composition is carbon clay which is covered in a plastic case and the leads are made of tinned copper. The main advantage of carbon resistors is that they are easily available at very low cost at all local vendors and the durability is good. The only disadvantage is that they are very sensitive to temperature.

Carbon resistors can be manufactured in wide range of values as low as 1 Ω value to a high value as 22 MΩ. Due to its low cost, they are used in circuits where cost is a criterion rather than the performance.

Working of a Resistor

The principle behind the working of resistor can be explained using hydraulic analogy. Let us imagine a pipe with water flowing through it. If we make the diameter of the pipe small, the flow of water is restricted. Now we increase the force of water through the same reduced diameter by increasing the pressure, then the energy will be dissipated in other form. The difference in pressure at both the ends of the pipe is significant. Now we apply this analogy to an electrical system i.e. force applied to water is comparable to current through a resistor and applied pressure is comparable to voltage.

The reason for this change in the form of energy can be explained as follows. The high electrical conductivity of metals is useful as it has free flow of electrons and this flow of charge is called electric current. But when the flow of electrons is not free i.e. restricted, the electrical energy is converted in to other forms like heat in case of poor conductors. This restriction of flow of electrons without completely stopping it is the idea behind resistors. This principle of restricted flow of electrons may not have to be used to get heat as output but has other functions like reduction in voltage or current, emission of light etc.

V-I Characteristics of a Resistor

V-I Characteristics of a resistor are the relation between the applied voltages and the current flowing through it. From Ohm’s law, we know that when the voltage applied across the resistor increases, the current flowing through it also increases i.e. the voltage applied is directly proportional to current. The V-I characteristics graph can be determined from the following circuit

The graph corresponding to the circuit for the function v(t) = R i(t) which is in the form of y = mx is as shown below. To plot the graph, the values of voltage (V) are taken on the y-axis and the values of current (I) are taken on the x-axis. From the graph it is clear that V-I characteristics of a resistor are linear and the value of the resistance at any instance can be determined by the slope of the curve at that instance.

The above specifications are valid in case of a pure resistance i.e. ideal resistor and the temperature is constant. In practical conditions, these values may vary depending on the operating environment and the characteristics might be different from the ideal linear values.

Variation of Resistance with Temperature

The effect of changes in temperature is a change in the value of resistance of the material. The reason for this change is not because of the variations in the dimensions of the material but rather the change in the resistivity of the material.

The flow of current in materials like conductors is the movement of electrons between atoms in the presence of an electric field. This is achieved by applying a potential difference across the conductor. This potential difference will cause the negatively charged electrons to move towards the positive terminal from atom to atom. These electrons which move freely between atoms are called free electrons. The conductivity of a material is dependent on the number of these free electrons in the atom of the material.

When there is a rise in the temperature, the heat will cause an atomic vibration and these vibrations will cause a collision between the free electrons and the electrons in the inner layers of the atom. These collisions will use the energy of free electrons. If more collisions take place, more energy of free electron is used and increases the resistance to flow of current. This is the case in conductors. In case of insulators the resistance decreases with increase in temperature. The reason is the availability of number of free electrons which are released from its captive stage.

In mathematical terms, a fractional change in resistance is directly proportional to the change in the temperature.

∆R/R0∝∆T

Where ∆R is the small change in resistance

∆R = R – R0

R is resistance at temperature T

R0 is resistance at temperature T0

∆T is change in temperature

∆T = T – T0

If we denote the proportionality constant in the above equation as alpha (α)

Then ∆R/R0 = α∆T

Where α is the temperature coefficient of the resistance.

The temperature coefficient of resistance is used to describe the relative change in resistance in association with change in temperature.

If the change in temperature is small then the above equation can be written as

R = R0 [1+α (T-T0)]

If the resistance increases with increase in temperature, then the material is said to be having a positive temperature coefficient. These materials are conductors.

If the resistance decreases with increase in temperature, then the material is said to be having a negative temperature coefficient. These materials are insulators.

The units of temperature coefficient are /0K or K-1.

Resistor Packages

Surface Mount Technology is technique where the components are directly placed on the surface of the circuit board. These components are called Surface Mount Devices. Resistors are also manufactured as SMDs. SMD Resistors are generally smaller with small leads or no leads. For contact purpose, they have metal contacts on either end.

The SMD resistors have two types of packages. They are two-terminal packaging and Metal Electrode Leadless Face packaging.

Initially, they have small leads through which the connections are made. Later, they have no leads, but have a metal contact on either ends of the device for connections.

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