Effect of Temperature On Resistance | Resistance Temperature Coefficient

Effect of Temperature On Resistance | Resistance Temperature Coefficient

Fundamental of Electrical Engineering | Effect of Temperature On Resistance| Resistance Temperature Coefficient

Effect of Temperature On Resistance:-

The electrical resistance changes with the change of temperature. The resistance does not only increase with the rise in temperature but it also decreases in some cases. In fact, for the different type of materials, the amount of change in resistance due to change in temperature is different which are discussed as follow.

Metal: The resistance of all pure metals increases linearly with increase in temperature over a limited temperature range. At low temperature, the ions are almost stationary. As the temperature increases, the ions inside the metal acquire energy and start oscillating about their mean positions. These vibrating ions collide with the electrons Hence resistance increases with increase in temperatures.

The resistance of all metals such as tungsten, copper, aluminum etc. increases linearly with increase in the temperature over a limited temperature range. For e.g. the resistance of copper is 100Ω at 0°c then it increases linearly upto 100°c. At a temperature of -234.5°c the resistance of copper is almost zero as shown in the figure.

Hence Pure metal have positive temperature Coefficient of Resistance.

Alloy: The resistance of almost all alloys increases with increase in temperature but the rate of change of resistance is less than that of metals. In fact, the resistance of certain alloys such as Manning, Eureka, and Constant show practically no change in resistance of a considerable range of temperature. Due to this property, the alloy is used to manufacture the resistance box.

Semiconductor, Insulator, and Electrolyte: The resistance of semiconductor, Insulator, and Electrolyte(silicon, Glass, Varnish etc) decrease with increase in temperature.At zero temperature, the semiconductor behaves as a perfect insulator.  As the temperature increases, some of the electrons acquire energy and become free for conduction. Hence, conductivity increase and resistance decrease with increase in temperature.

Semiconductor has negative temperature coefficient of resistivity therefore since with the increase in the temperature the resistance decreases.

 

Resistance Temperature Coefficient:

The change in resistance of a material with the increase in temperature can be expressed b means of the temperature coefficient of resistance.Consider a conductor having resistance Ro at 0°c and Rt at t°c. From the above discussion, we can conclude that the change in the resistance i.e (Rt – Ro) is

1. Directly proportional to the initial resistance Ro
2. Directly proportional to the rise in temperature t°c.
3. Depends on the nature of the material for conductor metals and alloy

Hence

(Rt – Ro) ∝ Rot

(Rt – Ro) = αRot

Rt  = Ro(1 + αot)

Where αo is constant and called as the temperature coefficient of resistance at 0°c and its value depends upon the nature of material and temperature.

Effect of Temperature On Temperature Coefficient of Resistance

Let Rt1 and Rt2 be the resistance of the conductor at t1°c and t2°c respectively, and α1 and α2 be the corresponding temperature coefficient. Let the conductor is heated from initial temperature t1°c to the final temperature t2°c.

Rt2  = Rt1[1 + αt1 (t2 – t1)]——————– 1

Now the same conductor is cooled from t2°c to t1°c.

Rt1  = Rt2[1 + αt2 (t1 – t2)]———————2

Substituting equation 2 in equation 1

Rt2  =  Rt2[1 + αt2 (t1 – t2)] [1 + αt1 (t2 – t1)]

Or

1 = [1 + αt2 (t1 – t2)] [1 + αt1 (t2 – t1)]

=  [1 – αt2 (t2 – t1)] [1 + αt1 (t2 – t1)]

Note: If the temperature changes from 0°C to t°C then

Effect Of Temperature On Resistivity

The specific resistance or resistivity of a material depends on temperature. The change in temperature affects the resistivity of a material in the same way as it affects the resistance.The resistivity of metals increases linearly with the increase in temperature. Let ρt1 and ρt2 be the resistivity at temperature t1°c and t1°c respectively. Let m be the slope of the linear part of the curve.

The ratio m/ρt1 is called the temperature coefficient of resistivity at t1°c and is almost equal to α1.

ρt2  = ρt1 [1 + αt1 (t2 – t1)]

Note: If the temperature changes from 0°C to t°C then

ρt  = ρo [1 + αot]

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Ques1. A piece of copper wire has a resistance of 50 Ω at 10°C. Whal is the maximum operating temperature if the resistance of the wire is to be increased by 20%? Assume α at 10°C = 0.0041°C-1.

Sol:- R1 = 50 Ω

R2 = 50 + 0.2 x 50 = 60Ω

t2 = Unkown temperature at which R2 will be 60Ω

Since

Rt2  = Rt1[1 + αt1 (t2 – t1)]

∴ R2  = R1[1 + α1 (t2 – t1)]

60 = 50[1 + 0.0041(t2 – 10)]

Ques 2. A certain winding made up of copper has a resistance of 100Ω at room temperature. if resistance temperature coefficient of copper at 0 °C is 0.00428 /°C, calculate the winding resistance temperature E increased to 50°C. Assume room temperature at 25°C.

R1 = 100 Ω

t1 = 25°C

t2 = 50°C

αo = 0.00428 /°C

Now

= 0.003866/°C

R2  = R1[1 + α1 (t2 – t1)]

R2  = 100[1 + 0.003866(50 – 25)]

=109.6657Ω

Principles of Electromechanical Energy Conversion

Principles of Electromechanical Energy Conversion:-

• Electromechanical Energy Conversion :- Conversion of other forms of energy in electrical form have many advantages like easy control, utilise, reliable, efficient etc. An electromechanical energy conversion device is one which converts electrical energy into mechanical energy and vice- versa.

Categories of various electromechanical energy conversion: -

(i) First category:- involves small motion, processes only low energy signals from electrical to mechanical or vice-versa. Example : telephone receivers, loud-speakers, microphone.

(ii) Second category:- consists of force or torque-producing devices with limited mechanical motion. Example: electromagnets, relays, moving-iron instruments.

(iii) Third category:- consists of continuous energy conversion devices. Example: generators and motors.

State electromechanical energy conversion. Also explain its significance:-

"Energy can neither be created nor be destroyed". One can only change its forms using appropriate energy conversion processes Energy conversion takes place between well known pairs of forms of energy.

1. Electrical- Chemical

2. Electrical -Thermal

3. Electrical- Optical

4. Electrical - Sound

5. Electrical- Mechanical

Electromechanical energy conversion is a process in which electrical energy is converted into mechanical energy or mechanical energy into electrical energy. The main advantage of the conversion is that energy in electrical form can be transmitted, utilized and controlled more reliably, easily and efficiently. Energy conversion derives are required at path ends of an electrical system, since energy is neither available and nor required in electrical form. Electromechanical energy conversion finds application in following categories of system:

(a) Transducers: Devices for obtaining signal for measurement/control.

(b) Force-producing devices : Solenoid-actuators, relays, electromagnets.

(c) Devices for continuous-energy conversion : Motor/generator.

Principle of Electromechanical Energy Conversion in rotating machines : - 

When energy is converted from one form to another, the principle of conversion of energy can be evoked. According to this principle, energy can neither be created nor destroyed, it can merely be converted from one form to another. In an energy conversion device, out of the total input energy, some energy is converted into the required form, some energy is stored and the rest is dissipated. In view of this, the energy balance equation must include these energy terms, and for a motor, it is:

(Total Electrical Energy Input) = (Mechanical Energy Output) + (Total Energy Stored) + (Total Energy Dissipated)

For generator action,

(Total Mechanical Energy Input) = (Electrical Energy Output) + (Total Energy Stored) + (Total Energy Dissipated)

So, the principle of en rgy conversion is based on energy balance. For a rotating machine

W elec. = W mech. - W fld.

Where,

W elect. → net electrical energy input

Wmech→ energy converted into mechanical form

Wfld.→ stored energy + energy losses (change in magnetic stored energy).

Add caption

V Curve of a Synchronous Motor:- 

                                V curve is a plot of the stator current versus field current for different constant loads. The Graph plotted between the armature current Ia and field current If at no load the curve is obtained known as V Curve. Since the shape of these curves is similar to the letter “V”, thus they are called V curve of synchronous motor.

The power factor of the synchronous motor can be controlled by varying the field current If. As we know that the armature current Ia changes with the change in the field current If. Let us assume that the motor is running at NO load. If the field current is increased from this small value, the armature current Ia decreases until the armature current becomes minimum. At this minimum point, the motor is operating at unity power factor. The motor operates at lagging power factor until it reaches up to this point of operation.

If now, the field current is increased further, the armature current increases and the motor start operating as a leading power factor. The graph drawn between armature current and field current is known as V curve. If this procedure is repeated for various increased loads, a family of curves is obtained.

The V curves of a synchronous motor are shown below.

The point at which the unity power factor occurs is at the point where the armature current is minimum. The curve connecting the lowest points of all the V curves for various power levels is called the Unity Power Factor Compounding Curve. The compounding curves for 0.8 power factor lagging and 0.8 power factor leading are shown in the figure above by a red dotted line.

The loci of constant power factor points on the V curves are called Compounding Curves. It shows the manner in which the field current should be varied in order to maintain constant power factor under changing load. Points on the right and left of the unity power factor corresponds to the over excitation and leading current and under excitation and lagging current respectively.

The V curves are useful in adjusting the field current. Increasing the field current If beyond the level for minimum armature current results in leading power factor. Similarly decreasing the field current below the minimum armature current result results in lagging power factor. It is seen that the field current for unity power factor at full load is more than the field current for unity power factor at no load.

The figure below shows the graph between power factor and field current at the different loads.

It is clear from the above figure that, if the synchronous motor at full load is operating at unity power factor, then removal of the shaft load causes the motor to operate at a leading power factor.

What is Capacitor? What is Capacitance?

There are three fundamental electronic components that form the foundation of a circuit – resistors, inductors, and capacitors. A capacitor in an electrical circuit behaves as a charge storage device. It holds the electric charge when we apply a voltage across it, and it gives up the stored charge to the circuit as when required. The most basic construction of a capacitor consists of two parallel conductors (usually metallic plates) separated by a dielectric material. 

When we connect a voltage source across the capacitor, the conductor (capacitor plate) attached to the positive terminal of the source becomes positively charged, and the conductor (capacitor plate) connected to the negative terminal of the source becomes negatively charged. Because of the presence of dielectric in between the conductors, ideally, no charge can migrate from one plate to other.

So, there will be a difference in charging level between these two conductors (plates). Therefore an electric potential difference appears across the plates. The charge accumulation in the capacitor plates is not instantaneous rather it is gradually changing. The voltage appears across the capacitor exponentially rises until it becomes equal to that of the connected voltage source.

Capacitance:-

Now we understand that the charge accumulation in the conductors (plates) causes the voltage or potential difference across the capacitor. The quantity of charge accumulated in the capacitor for developing a particular voltage across the capacitor is referred to as the charge holding capacity of the capacitor. We measure this charge accumulation capability of a capacitor in a unit called capacitance. The capacitance is the charge gets stored in a capacitor for developing 1 volt potential difference across it. Hence, there is a direct relationship between the charge and voltage of a capacitor. The charge accumulated in the capacitor is directly proportional to the voltage developed across the capacitor.

Where Q is the charge and V is the voltage.

Here C is the constant of proportionality, and this is capacitance,

The capacitance depends upon three physical factors, and these are the active area of the capacitor conductor (plates), the distance between the conductors (plates) and permittivity of the dielectric medium.

Here, ε is permittivity of the dielectric medium, A is the active area of the plate and d is the perpendicular distance between the plates .

Capacitance of plates capacitor:-

The capacitance (C) of the plates capacitor is equal to the permittivity (ε) times the plate area (A) divided by the gap or distance between the plates (d):

 

C is the capacitance of the capacitor, in farad (F).

ε is the permittivity of the capacitor's dialectic material, in farad per meter (F/m).

A is the area of the capacitor's plate in square meters (m²).

d is the distance between the capacitor's plates, in meters (m).

Single Phase Voltage Transformer:-

Transformer:-

Single Phase Voltage Transformer:-

In other words, for a transformer there is no direct electrical connection between the two coil windings, thereby giving it the name also of an Isolation Transformer. Generally, the primary winding of a transformer is connected to the input voltage supply and converts or transforms the electrical power into a magnetic field. While the job of the secondary winding is to convert this alternating magnetic field into electrical power producing the required output voltage as shown.

Transformer Construction (single-phase):-

• Where:
•   VP  –  is the Primary Voltage
•   VS  –  is the Secondary Voltage
•   NP  –  is the Number of Primary Windings
•   NS  –  is the Number of Secondary Windings
•   Φ (phi)  –  is the Flux Linkage

Notice that the two coil windings are not electrically connected but are only linked magnetically. A single-phase transformer can operate to either increase or decrease the voltage applied to the primary winding. When a transformer is used to “increase” the voltage on its secondary winding with respect to the primary, it is called a Step-up transformer. When it is used to “decrease” the voltage on the secondary winding with respect to the primary it is called a Step-down transformer.

However, a third condition exists in which a transformer produces the same voltage on its secondary as is applied to its primary winding. In other words, its output is identical with respect to voltage, current and power transferred. This type of transformer is called an “Impedance Transformer” and is mainly used for impedance matching or the isolation of adjoining electrical circuits.

The difference in voltage between the primary and the secondary windings is achieved by changing the number of coil turns in the primary winding ( NP ) compared to the number of coil turns on the secondary winding ( NS ).

As the transformer is basically a linear device, a ratio now exists between the number of turns of the primary coil divided by the number of turns of the secondary coil. This ratio, called the ratio of transformation, more commonly known as a transformers “turns ratio”, ( TR ). This turns ratio value dictates the operation of the transformer and the corresponding voltage available on the secondary winding.

It is necessary to know the ratio of the number of turns of wire on the primary winding compared to the secondary winding. The turns ratio, which has no units, compares the two windings in order and is written with a colon, such as 3:1 (3-to-1). This means in this example, that if there are 3 volts on the primary winding there will be 1 volt on the secondary winding, 3 volts-to-1 volt. Then we can see that if the ratio between the number of turns changes the resulting voltages must also change by the same ratio, and this is true.

Transformers are all about “ratios”. The ratio of the primary to the secondary, the ratio of the input to the output, and the turns ratio of any given transformer will be the same as its voltage ratio. In other words for a transformer: “turns ratio = voltage ratio”. The actual number of turns of wire on any winding is generally not important, just the turns ratio and this relationship is given as.