Test: Resistivity Temperature Coefficient of Resistance - Electrical Engineering (EE) MCQ

Conductors are materials(mostly metals), which freely allow the passage of electrons through it. If electrons can flow freely through a material, it implies that even current can flow freely through that material since current is the rate of flow of electrons.

Resistance is directly proportional to the length of the wire, hence as the length of the wire increases, resistance increases.

Resistance is inversely proportional to area of cross section. As area of cross section increases, resistance decreases. Hence the 10sqm wire has higher resistance than the 15sqm wire.

The expression for resistance is: Resistance=Resistivity*length of wire/ area of cross section of wire. Hence resistance is directly proportional to length.

From the given circuit, R=V/I= 200/5 =40ohm.
Resistivity= Resistance*Area of cross section/ Length of the wire.
Resistivity= 40*2/10= 8 ohm-metre.

Resistivity= RA/l= ohm*metre²/metre. Hence the unit of resistivity is ohm- metre.

Resistivity is a material property. Different materials have different resistivity’s. Resistivity depends on the material of the wire, hence the resistivity of copper is 1.59*10^-8ohm^-metre.

Resistivity of first wire= RA1/l= 2R/l.
Resistivity of second wire= RA2/l = 5R/l.
Ratio of the first resistance to the second= (2A/l)/(5A/l)= 2/5.

Resistance is a temperature dependent element. As the temperature increases, resistance also increases, hence resistance depends on temperature.

The expression for resistivity is= RA/l. The expression for conductivity= Cl/A; C=1/R => Conductivity= l/(AR) = 1/resistivity. Hence, conductivity is the reciprocal of resistivity.

In a conductor, the valence band and conduction band overlap each other, there is an excess of electrons in the conduction band. When the temperature increases, there is an overcrowding of electrons in the conduction band hence reducing the mobility and hence resistance increases.

In case of an insulator, the energy gap between the conduction band and the valence band is very large. When the temperature is increased, the electrons move from the conduction band to the valence band and hence it starts conducting. When conductance increases, resistance decreases, since C=1/R. Thus, when temperature increases, resistance decreases in insulators.

The resistance of metals increases with an increase in temperature thus, it has a positive temperature coefficient.

Insulators have a negative temperature coefficient because as temperature increases, the resistance of insulators decreases.

: R=Reff[1+temp. coeff(T-Teff)].
From the given expression: (R/Reff-1)/(T-Teff)= temp. coeff. Hence, the unit is the reciprocal of that of temperature= centigrade^-1.

The temperature coefficient of copper is 0.00428 centigrade^-1
R1=R0(1+temp. coeff.*T1)= 200(1+0.00428*80)= 268.5 ohm.

Caloriemeter measures the amount of heat and not the temperature of coil coefficient. Temperature of a coil is mainly measured by thermometer.

The rise or fall in resistance with rise in temperature depends upon the property of the material. Hence it rises with temperature in metals and falls with temperature in insulators and semi-conductors.

When the temperature keeps increasing, the resistance keeps falling continuously and hence the current to increase. This causes the heat in the semi-conductor to rise. This causes the temperature to increase further and the resistance to further decrease. This process continues and until there is sufficient heat to destroy the structure of the semi-conductor completely. This is known as thermal runway.

When the temperature of a material falls to absolute zero, the resistance falls to zero and hence there are no I2R losses. Since resistance is zero, conductance is almost infinity and hence these materials are known as superconductors.