ET Lesson No 9: Resistance

ET Lesson No 9: Resistance

Definition of Resistance

The property of a substance to resist the flow of current through it is called resistance.

When a voltage is applied across a substance there will be an electric current through it. The applied voltage across the substance is directly proportional to the current through it. The constant of proportionality is resistance. Hence resistance is defined as the ratio of the applied voltage to the current through the substance.

Where V is voltage, I is current and R is resistance.

Concept of Resistance

To understand the matter let us take examples of metallic substances. There are numbers of free electrons moving randomly in the crystal structure of a metallic substance. When a voltage is applied across the resistance due to the electric field the free electrons drift from lower potential point to higher potential point in the substance. During drifting motion, the free electrons continually collide with atoms of the substance and this phenomenon prevents the free motion of electrons and this causes resistance.

Unit of Resistance

From the definition of resistance, it can be said that the unit of electric resistance is volt per ampere. One unit of resistance is such a resistance which causes 1 ampere current to flow through it when 1 volt potential difference is applied across the resistance. The unit of electric resistance that is volt per ampere is called ohm(Ω) after the name of great German physicist George Simon Ohm.

He is famous for his law called Ohm’s law which is applicable only on pure resistance. The unit ohm is normally used for moderate values of resistance but there may be a very large as well as a very small value of resistance used for different purposes. These values are expressed in giga-ohm, mega ohm, kilo-ohm, milli-ohm, micro-ohm even in nano-ohm range depending on the value of resistance.

Unit Name	Abbreviation	Value in ohm (Ω)
Giga Ohm	G Ω	109 Ω
Mega Ohm	M Ω	106 Ω
Kilo Ohm	K Ω	103 Ω
Milli Ohm	m Ω	10 – 3 Ω
Micro Ohm	μ Ω	10 – 6 Ω
Nano Ohm	n Ω	10 – 9 Ω

Resistance of Different Materials

Depending on the resistance value substances are divided into three categories.

There are some materials mainly metallic substances that offer very low resistance to the current through them. These substances are referred to as conductors more precisely electrical conductors. Silver is an extremely good conductor of electricity but it is not widely used in electrical systems because of its high cost. Aluminum is a good conductor and it is a commonly used conductor because of its low cost and plenty of availability. Copper is another good conductor commonly used in different electronics and electrical circuits and it is a better conductor than aluminum but at the same time, it is costlier than aluminum.

There is another category of materials called semiconductors. These have a moderate value of resistance i.e. not very high as well as not very low at room temperature. There are endless uses of semiconductors for making electrons devices. Silicon, germanium are two mostly used semiconductor materials. In addition to these different compounds also behave as semiconductors.

The materials offer extreme resistance to the current is known as the insulator or electrical insulation material. These materials are a very bad conductor of electricity and mainly used to prevent leakage current in electric systems. Papers, dry woods, mica, porcelain, glass epoxy polyester, mineral oil, SF6 gas, Nitrogen gas, other gases, air, etc are very good examples of insulation materials.

Effect of Temperature on Resistance

In metallic substances with rising temperature the interatomic vibrations increase and hence offer more resistance to the movement of electrons causing the current. Hence, with increasing temperature the resistance of metallic substances increases. The temperature coefficient of resistance is positive for these materials. In semiconductors with increasing temperature the number of free electrons increases as at higher temperature more number of covalent bonds gets broken to contribute free electrons in the substance. This reduces the resistance of the substance. Hence semiconductors have a negative temperature coefficient of resistance.There are some materials mainly metals, such as silver, copper, aluminum, which have plenty of free electrons. Hence this type of materials can conduct current easily that means they are least resistive. But the resistivity of these materials is highly dependable upon their temperature. Generally metals offer more electrical resistance if temperature is increased. On the other hand the resistance offered by a non-metallic substance normally decreases with increase of temperature.

If we take a piece of pure metal and make its temperature 0' by means of ice and then increase its temperature from gradually from 0'C to to 100'C by heating it.

During increasing of temperature if we take its resistance at a regular interval, we will find that electrical resistance of the metal piece is gradually increased with increase in temperature. If we plot the resistance variation with temperature i.e. resistance Vs temperature graph, we will get a straight line as shown in the figure below. If this straight line is extended behind the resistance axis, it will cut the temperature axis at some temperature, – t0 'C. From the graph it is clear that, at this temperature the electrical resistance of the metal becomes zero. This temperature is referred as inferred zero resistance temperature.

Although zero resistance of any substance cannot be possible practically. Actually rate of resistance variation with temperature is not constant throughout all range of temperature. Actual graph is also shown in the figure below.

Let’s R1 and R2 are the measured resistances at temperature t1'C and t2'C respectively. Then we can write the equation below,

From the above equation we can calculate resistance of any material at different temperature. Suppose we have measured resistance of a metal at t1'C and this is R1.

If we know the inferred zero resistance temperature i.e. t0 of that particular metal, then we can easily calculate any unknown resistance R2 at any temperature t2'C from the above equation.

The resistance variation with temperature is often used for determining temperature variation of any electrical machine. For example, in temperature rise test of transformer, for determining winding temperature rise, the above equation is applied. This is impossible to access winding inside the an electrical power transformer insulation system for measurement of temperature but we are lucky enough that we have resistance variation with temperature graph in our hand. After measuring electrical resistance of the winding both at the beginning and end of the test run of the transformer, we can easily determine the temperature rise in the transformer winding during test run.

20'C is adopted as standard reference temperature for mentioning resistance. That means if we say resistance of any substance is 20Ω that means this resistance is measured at the temperature of 20'C.

Resistivity or Coefficient of Resistance

Resistivity or Coefficient of Resistance is a property of substance, due to which the substance offers opposition to the flow of current through it. Resistivity or Coefficient of Resistance of any substance can easily be calculated from the formula derived from Laws of Resistance.

Laws of Resistance

The resistance of any substance depends on the following factors,

Length of the substance.
Cross sectional area of the substance.
The nature of material of the substance.
Temperature of the substance.

There are mainly four (4) laws of resistance from which the resistivity or specific resistance of any substance can easily be determined.

First Law of Resistivity

The resistance of a substance is directly proportional to the length of the substance. electrical resistance R of a substance is

Where L is the length of the substance.

If the length of a substance is increased, the path traveled by the electrons is also increased. If electrons travel long, they collide more and consequently the number of electrons passing through the substance becomes less; hence current through the substance is reduced. In other words, the resistance of the substance increases with the increasing length of the substance. This relation is also linear.

Second Law of Resistivity

The resistance of a substance is inversely proportional to the cross-sectional area of the substance. Electrical resistance R of a substance is

Where A is the cross-sectional area of the substance.

The current through any substance depends on the numbers of electrons pass through a cross-section of substance per unit time. So, if the cross section of any substance is larger then more electrons can cross the cross section. Passing of more electrons through a cross-section per unit time causes more current through the substance. For fixed voltage, more current means less electrical resistance and this relation is linear.

Resistivity

Combining these two laws we get,

Where ρ (rho) is the proportionality constant and known as resistivity or specific resistance of the material of the conductor or substance. Now if we put, L = 1 and A = 1 in the equation, we get, R = ρ. That means resistance of a material of unit length having unit cross – sectional area is equal to its resistivity or specific resistance. Resistivity of a material can alternatively be defined as the electrical resistance between opposite faces of a cube of unit volume of that material.

Third Law of Resistivity

The resistance of a substance is directly proportional to the resistivity of the materials by which the substance is made. The resistivity of all materials is not the same. It depends on the number of free electrons, and size of the atoms of the materials, types of bonding in the materials and many other factors of the material structures. If the resistivity of a material is high, the resistance offered by the substance made by this material is high and vice versa. This relation is also linear.

Fourth Law of Resistivity

The temperature of the substance also affects the resistance offered by the substance. This is because, the heat energy causes more inter-atomic vibration in the metal, and hence electrons get more obstruction during drifting from lower potential end to higher potential end. Hence, in metallic substance, resistance increases with increasing temperature. If the substance in nonmetallic, with increasing temperature, the more covalent bonds are broken, these cause more free electrons in the material. Hence, resistance is decreased with increase in temperature.

That is why mentioning resistance of any substance without mentioning its temperature is meaningless.

Unit of Resistivity

The unit of resistivity can be easily determined form its equation

The unit of resistivity is Ω – m in MKS system and Ω – cm in CGS system and 1 Ω – m = 100 Ω – cm.

List of Resistivity of Different Commonly Used Materials

Materials	Resistivity in μ Ω – cm at 20oC
Aluminium	2.82
Brass	6 to 8
Carbon	3k to 7k
Constantan	49
Copper	1.72
Gold	2.44
Iron	12.0
Lead	22.0
Manganin	42 to 74
Mercury	96
Nickel	7.8
Silver	1.6
Tungsten	5.51
Zinc	6.3

More than one electrical resistance can be connected either in series or in parallel in addition to that, more than two resistances can also be connected in combination of series and parallel both. Here we will discuss mainly about series and parallel combination.

Resistances in Series

Suppose you have three different types of resistors – R1, R2 and R3 – and you connect them end to end as shown in the figure below, then it would be referred as resistances in series. In case of series connection, the equivalent resistance of the combination, is sum of these three electrical resistances.

That means, resistance between point A and D in the figure below, is equal to the sum of three individual resistances. The current enters in to the point A of the combination, will also leave from point D as there is no other parallel path provided in the circuit.

Now say this current is I. So this current I will pass through the resistance R1, R2 and R3. Applying Ohm’s law, it can be found that voltage drops across the resistances will be V1 = IR1, V2 = IR2 and V3 = IR3. Now, if the total voltage applied across the combination of resistances in series, is V.

Then obviously

Since, sum of voltage drops across the individual resistance is nothing but the equal to applied voltage across the combination.

Now, if we consider the total combination of resistances as a single resistor of electric resistance value R, then according to Ohm’s law,

V = IR ………….(2)

Now, comparing equation (1) and (2), we get

So, the above proof shows that equivalent resistance of a combination of resistances in series is equal to the sum of individual resistance. If there were n number of resistances instead of three resistances, the equivalent resistance will be

Resistances in Parallel

Say we have three resistors of resistance value R1, R2 and R3. These resistors are connected in such a manner that the right and left side terminal of each resistor is connected together, as shown in the figure below.

This combination is called resistances in parallel. If electric potential difference is applied across this combination, then it will draw a current I (say).

As this current will get three parallel paths through these three electrical resistances, the current will be divided into three parts. Say currents I1, I1 and I1 pass through resistor R1, R2 and R3 respectively.

Where total source current

Now, as from the figure it is clear that, each of the resistances in parallel, is connected across the same voltage source, the voltage drops across each resistor is the same, and it is same as supply voltage V (say).

Hence, according to Ohm’s law,

Now, if we consider the equivalent resistance of the combination is R.

Then,

Now putting the values of I, I1, I2 and I3 in equation (1) we get,

The above expression represents equivalent resistance of resistor in parallel. If there were n number of resistances connected in parallel, instead of three resistances, the expression of equivalent resistance would be