CHANGE OF RESISTANCE WITH TEMPERATURE

Resistance of all materials is affected by changes in temperature. Non-conductors or insulators usually decrease in resistance with an increase in temperature. 

For example - glass is an insulator when cold, and become a fairly good conductor when red hot.

Mostly metallic conductors increase in resistance with an increase in temperature. This is for all metals. Alloys differ in this characteristic, some showing practically no change in resistance with the change of temperature. Manganin (an alloy of copper manganese and nickle) changes its resistance by 0.001% per degree centigrade. Carbon decreases in resistance with increase in temperature.

If the resistance of pure meal is plotted against temperature (see figure), it is found that the graph is practically a straight line for a range say 0° C.

If this curve is extended to the left, it cuts the temperature axis at a certain temperature say - T₀ degree.

This point is found to be -234.5° C for annealed copper of 100% conductivity.

This does not mean copper has zero resistance at this temperatures around -234.5° C, through very low.

In practice, the resistance-temperature graph (or characteristics) deviates from the straight line by a marked degree at a very low as well as high temperatures.

Within the usual working range of temperature, however, a straight line relation may be assumed with little error. (The value of T₀ for aluminium is -228.2° C.)

ELECTRIC CIRCUITS

Just as water flows in a pipe from a higher level (or higher pressure) to a lower level, so do the electrons in a conductor. They flow from a point of higher potential to a point of lower potential. The path followed by the electrons is called the electric circuit.

If a material having free electron (such as copper, silver, etc.) as connected between the terminals of a battery, having an e.m.f. the electrons in the material  being negatively charged, are continuously attracted to the positive terminal of the battery and repelled by the negative terminal. The flow of electrons, (as mentioned earlier) will constitute an electric current.

Although the drift of the electrons in the material is towards the positive terminal of the battery, the direction of the current is taken as opposite to the electron movement. This direction of current has universal acceptance and is known as the conventional current, whereas the term "electronic current" is used by those who depart from this convention. The people consider electron movement and current direction to be the same.

Above diagram shows an Electric Circuit. This is a closed circuit. But if a switch is introduced in one of the connecting wires between connections are more complex, a circuit may have open circuit part as well as a closed circuit part; then the whole arrangement is called either circuit or a network.

SPECIFIC RESISTANCE OR RESISTIVITY

The Specific Resistance or Resistivity of a material depends upon the nature and composition of the material.

From the relation ,

if  l = 1 m and A = 1 sq m

then R = 𝜌.

Hence, the specific resistance of a conductor may be defined as the resistance offered by unit m cube of the material of the conductor.

It can also be defined as the resistance of a conductor of 1 m length and 1 sq m cross-sectional area.

The unit of resistance is ohm-m or ohm per m³. 

If the unit of length is in cm,  then the unit of resistivity is ohm-cm or ohm-cm³.

CONDUCTANCE AND UNIT OF CONDUCTANCE - MHO

Conductance: Conductance is a measure of the ease with which the current will flow through a substance.

Conductance is usually denoted by G.

So, this is the reciprocal of resistance, 

i.e.                                

Appropriately, the unit of conductance is termed mho() i.e. the unit of resistance (ohm) spelled backwards.

EFFECT OF TEMPERATURE ON RESISTANCE OF VARIOUS TYPES OF MATERIALS

The effect of rise of temperature on electrical resistance is not always an increase in resistance but sometimes there is a decrease in resistance also.

The effect of temperature on different types of materials can be classified as follows:

(i) Pure Metals: With a rise in temperature, the resistance of pure metals increases and ∝, the temperature coefficient of resistance is said to be positive.

(ii) Insulators, Electrolytes, etc: In the case of insulators, semi-conductors and electrolytes the electrical resistance decreases with a rise in temperature and ∝ in such cases is said to be negative.

(iii) Alloys: The resistivity of an alloy is usually considerably greater than that of its constitute metals and its ∝ is ordinarily very small and irregular. For many purposes the temperature coefficient of resistance of alloys such as Eureka (Cu  60% + Ni  40%) and Manganincalloy of Copper + Magnganese + Nickle) and constantine is taken as negligible. 

RESISTANCE AND UNIT OF RESISTANCE - OHM

Resistance: "The flow of electrons through a conductor is opposed by the conductor. Since this flow of electrons constitutes a current, the flow of a current is offered opposition by the conductor. This property of the conductor due to which it opposes or resists the flow of electrons is called Resistance."

A device whose chief property is to oppose or resist is called Resistor. And If the opposition is variable, the device is called a variable resistance or a Rheostat.

The unit of Resistance is ohm (𝛺) and it is pronounced as omega.

A conductor is said to offer a resistance of 1 ohm, when it allows a current of 1 ampere to flow through it when 1 volt of potential is applied across its terminals.

When the resistances are too high (e.g., for insulators) to be measured in ohms, one may employ the unit kilo-ohms (K𝛺) or mega-ohms (M𝛺). If the resistances are very small (less than an ohm), units such as milli ohm (10⁻³ 𝛺) or micro-ohm (10⁻⁶ 𝛺) are used.

In an electrical formula, the letter "R" generally stands for the resistance of a conductor.

ELECTRIC FIELD

Electric Field: If electric charges in a space experiences force, the space contains an electric field and if these forces move the charges from one point to another, work is said to be done on them.

ELECTROMOTIVE FORCE (E.M.F.)

Electromotive Force: Electromotive Force (emf) is the force which creates the pressure that causes the current to flow through a conductor.

Its unit is a volt and is defined as the emf necessary to cause one ampere of current to flow through a resistance of one ohm

Electric Pressure is also called voltage or potential. Where the unit of volt is too large, we may use the milli-volt (mV) which is one thousandth (1/1000) of a volt or the micro-volt (𝜇V) which is (1/1000000) of a volt. Sometimes it is more conventional to use very high voltage unit, called as kilo-volt (kV), which is equal to 1000 volts.

Voltage or potential difference between two points is denoted by V.

ELECTRIC CURRENT

The amount of positive charge equals the amount of negative charge and therefore an atom always behaves neutrally.

If an electron is removed from a neutral atom, this atom becomes positively charged and is called a Positive ion. On the other hand, if an electron is added to a neutral atom, it becomes negatively charged and is called a Negative ion. Thus atoms which have lost or gained one or more electrons are called Ions.

Between any two ions, there exists a stress or field of force. Similarly charged ions repel whereas disimilarly charged ions tend to attract each other. Generally, this field of force is called the electric, dielectric or electrostatic field.

The movement of ions arising from the presence of this field is called the Electric Current.

OHM'S LAW

Ohm's Law: This law gives the relation between the potential difference V and the current I flowing through a conductor.

It may be stated as:

"For a given conductor the ratio of the steady direct potential difference V between its ends to the steady direct electric current I flowing through the conductor, is a constant, provided the physical conditions of the conductor , for example- temperature, etc., remain unchanged."

This Law, however, is also applicable to AC circuits.

It can be represented by

                       

or                    

or                    

or                    

or                    

where R is a constant for the conductor and is called its electrical resistance or resistance of the conductor

The quantities V, I and R measured in volts, amperes, and ohms respectively.

From the above relation of Ohm's law i.e., V = I R , it may be deduced that a conductor is said to offer a resistance of one ohm, when a unit potential difference (1 volt) applied across its ends, causes a unit current (1 ampere) to flow through it.