#### Resistor Power Rating

#### Introduction

Resistors can be rated based on two values. First is based on the resistance of the resistor. Second is based on the power in Watts that a resistor can dissipate safely.

The power rating of a resistor can be defined as the loss of electrical energy in the form of heat in a resistor when a current flows through it in the presence of a voltage.

Resistors can be used in any circuit based on the requirement in any combination of current and voltage. These different combinations of currents and voltages are selected such that the dissipating power rating of a resistor does not exceed the resistor power rating, which indicates the amount of power a resistor can convert into heat without causing any damage to it. The resistor power rating can also indicate the amount of power a resistor can absorb without causing any damages.

The Resistor Power Rating is also called as Resistor Wattage Rating. The Resistor Power Rating is defined as “the amount of heat a resistor can dissipate for an indefinite time period without affecting or degrading its performance.”

The resistor power rating is measured in Watts which are the units of power.

Since the power dissipation is dependent on the size of the object, the resistor power rating can vary from a value as small as one tenth of a Watt to a large value as hundreds of Watts based on the size, temperature and construction procedure of resistor.

Generally the temperature used to define the power rating is ambient temperature or room temperature. Generally, most of the resistors have their maximum power rating at an ambient temperature of 70^{0}C or less.

### Power Dissipation

Resistors are basic electrical components which obey Ohm’s Law. When a voltage V is applied between the leads of the resistor of resistance R, a current I flows through it. This current I is given by

I = V / R

The movement of electrons is the cause for this current and they are accelerated by the electric field due to the applied potential. These accelerated electrons which possess kinetic energy, try to move towards the positive side of the material and in this process they collide with atoms and lose their energy. And the result of this collision is conversion of electrical energy to heat.

The rate of loss of energy or power dissipation can be calculated from the formula P = I * V.

These three quantities of current, voltage and power can be superimposed into a triangle called Power Triangle. In this triangle, the power which is an indication of heat dissipated in the resistor is at the top of the triangle.

The current consumed and the voltage applied are placed at the bottom.

The figure of power triangle is shown below

From this triangle the power dissipated in a resistor can be calculated if the values of voltage across it and current flowing through it are known. The triangle is used to mathematically represent the relation between Power, Current and Voltage.

The power is calculated as

P = I * V

The current is calculated as

I = P / V

The voltage is calculated as

V = P / I

Ohm’s law can be used to calculate the power dissipated in a resistor if the value of resistance of the resistor is known. If any two values among voltage, current and resistance are known, then the equation of power can be written using Ohm’s law.

P = I * V

From Ohm’s Law, we have

V = I * R

Therefore,

P = I^{2} * R

And P = V^{2} / R

Hence the power dissipation in a resistor can be calculated using any of the following standard equations

Power P = V * I

P = I

^{2}* RP = V

^{2}/ R

where,

P is power in Watts

V is Voltage across resistor in Volts

I is Current flowing through the resistor in Amperes

R is Resistance of resistor in Ohms.

#### Power Dissipated by a Resistor

To find the power dissipated by a resistor, a resistor of resistance R is considered. Let a potential or voltage of V be applied across the length of the resistor. Let Q be the charge passing through a conductor or resistor in this case, in unit time. Then by the definition of current which is rate of flow of charge, the current I flowing in the resistor is given by

I = Q / t

==> The charge can be written as Q = I * t

Where t is the time in seconds.

If a potential of V is applied between the ends of the resistor, then the energy lost in the form of heat during the flow of current is given by

Q * V.

Let E be the energy that is lost in the form of heat.

Then E = Q * V

Using the equation Q = I * t in the above equation

We get E = I * t * V

Power can be defined as rate of doing work. In this context, power is defined as a rate at which electrical energy is converted to heat.

∴ P = E / t = I * V

Power lost in terms of heat or power dissipation is,

P = I * V

This can be rewritten in many ways with the help of Ohm’s law (V = I * R).

P = I * V = I^{2} * R = V^{2} / R

#### Units of Power

The unit of current is ampere which is Coulomb per second. The unit of voltage is volt which is Joule per Coulomb.

Therefore the units of power can be derived by taking current times voltage. This is the amount of energy used per unit charge time’s number of unit charges passing per second.

∴ ampere * volt = (Coulomb / Second) * (Joule / Coulomb) = Joule / Second.

This is rate of flow if energy and given the name Watt.

Watt = Joule / second.

Using Ohm’s law, the equation of Power and its units can be written as follows

P = V * I => Units of power = Volts * Amps

P = I^{2} * R => Units of power = Amps^{2} * Ohms

P = V^{2} / R => Units of power = Volts^{2} / Ohms

### Power Resistors

Power rating of a resistor defines the permissible amount of heat that can be dissipated by a resistor. Every resistor has a predefined power rating and this is determined by considering various factors like type of material and surface area.

The power ratings are mentioned in the units of watts and some of the available standard power ratings of resistors are 0.25W, 0.5W, 1W, 2W, 5W, etc.

When a resistor has a power rating of 2W, a maximum of 2W power can be fed to it for all combinations of voltage and currents as long as possible.

Some resistors are designed for larger power dissipation. These are called Power Resistors. Resistors with power rating of at least 5W come under power resistors. The material used for construction of power resistors must be of high thermal conductive in nature. Power resistors often come with heat sink which helps them in dissipation of heat.

Wire wound power resistors are common, but they can also be found in other types. If Nichrome alloy based wire wound resistors are used with proper non-conductive enamel paint, they can withstand temperatures up to 450^{0}C.

Another type of resistors used to withstand large amounts of currents is Grid Resistors. Grid Resistors can withstand a current up to 500 Amps and can have a resistance values as low as 0.04 Ω. The construction of Grid Resistors includes two electrodes with large metal stripes connected between them in the form of a matrix. Grid resistors are used as grounding resistors, brake resistors and harmonic filters for electric substations.

Another type of power resistors are Water Resistors. The construction includes tubes which carry saline solution with electrodes connected at both ends of the tube. The concentration of saline solution or salt water will determine the resistance. Because of the presence of water in the tubes, water resistors provide large heat capacity, which in turn result in high power dissipation.

Power resistors can also be made in the form of Surface Mounted Devices. Because of their small size, the power dissipation capacity of SMD resistors is less than grid type resistors and water resistors. Usually the power dissipated by SMD resistors is in the order of few Watts.

The range of power dissipated by different types of power resistors are as follows- SMD Resistors - 5 W or less
- Helical Wound - 50 W or less
- Edge Wound - 3.5 KW or less
- Grid Resistors - 100 KW or less
- Water Resistors - 500 KW or less

#### Power Rating Examples

1. For example, to choose an appropriate power rated resistor of resistance 800 Ω and a supply voltage of 12 V. The available power ratings are 0.25 W, 0.5W and 1 W.

Power P in the resistor is equal to P = V^{2} / R

Therefore P = (12)^{2} / 800 = 0.18 W.

Hence a resistor of Power rating 0.25 should be used.

2. If a resistor with 12 V supply and current of 100mA is used then its maximum power rating is

P = V * I

P = 12 * 100 * 10^{-3}

P = 1.2 W

^{}

#### Applications of Power Resistors

Every resistor is rated with its maximum power rating. This power rating indicates the maximum power a resistor can dissipate without causing any damages to itself or the circuit. Some applications require less power dissipation and others require large power dissipation. Power resistors are used in applications where we need to dissipate large power. Some of the applications of Power resistors are

- Engine brakes in heavy locomotives and trams use power resistors. Locomotives move at high speed and possess high kinetic energy. While stopping these high speed locomotives, their kinetic energy is converted to heat. Depending on the velocity of the locomotives, the amount of heat generated can be in the order of few Kilo Watts. Classic disc brakes can’t be used as they wear out easily. Hence regenerative brakes or high power resistors in the form of Grid resistors are used in locomotives.
- Power resistors are used as grounding resistors to limit fault currents, high voltages and act as protective relays. These resistors can be rated up to 8 Kilo Amps.
- Power resistors are used as load resistors in turbines and Uninterruptable Power Supplies. They can be designed to provide adjustable resistance and can dissipate a power of up to 6 Mega Watts. Because of this high power dissipation, load resistors are equipped with an efficient cooling system to control the temperature and prevent the devices from burning out.

Resistors are used for many applications in a circuit. But all resistors are not suitable for all the applications. Resistors are selected using different parameters.

Resistor color codes helps to read resistance, tolerance and voltage. Other than these three values, there is another important parameter required, for using the resistor in a circuit. This is power rating of a resistor.It is very important to use correct power rated resistor in the circuit to prevent the circuit from damaging.

### What is the meaning of power rating?

- Resistor power rating can be defined as the maximum power a resistor can handle safely without any damage.
- We know that, resistor dissipates the excess energy in form of heat. Power rating indicates the maximum heat a resistor can dissipate safely.
- Increasing the power more for few percent than rating, will burn the resistor.

### How resistors are rated?

- The resistor power rating is rated in watts, which are units of power. Hence it is also termed as wattage.
- Generally, larger the resistor more power it can handle.
- As the wattage of the resistor increases cost also increases.
- Resistors generally start from 1/8th watt to many kilo watts.Resistor wattage can be noticed by seeing the size of the resistor.

Resistors with high wattage are called power resistors. Below is the figure showing resistors with their wattage.

### How to determine wattage of a resistor?

Electrical power is given as P=V x I

Where v is voltage

I is current

From Ohm’s Law, we have V = I × R

Where R is resistance

Therefore P = I^{2} × R

And P = V^{2} / R

Hence the power dissipation in a resistor can be calculated using any of the following standard equations

- Power P = V × I
- P = I
^{2}× R - P = V
^{2}/ R

Here is example to calculate the resistor rating to be used in a circuit.

Consider a circuit powering a led with a source voltage of 12v and resistance of 800 ohms. Now calculate what wattage resistor can be used in the circuit?

We know V= 12v ,R=800 ohms.Now calculating the current

I=V/R=12/800 = 0.015=15 mA current.

Thus power dissipated by the resistor is calculated using P= 12x15x10^{-3} =0.18 watts

Hence a 1/4th watt resistor must be used here. Using 1/8th watt resistor will damage the circuit.

### Power Resistors

- Resistors that are designed to handle high power are called power resistors.
- Resistors with power rating of at least 5W come under power resistors.
- The material used for construction of power resistors must be of high thermal conductive in nature.
- Power resistors often come with heat sink which helps them in dissipation of heat.

#### Wire wound power resistors

- Wire wound power resistors are common, but they can also be found in other types.
- If Nichrome alloy based wire wound resistors are used with proper non-conductive enamel paint, they can withstand temperatures up to 450
^{0}C.

#### Grid Resistors

- Grid Resistors are used to withstand large amounts of currents .
- They can withstand a current up to 500 Amps and can have a resistance values as low as 0.04 Ω.
- The construction of Grid Resistors includes two electrodes with large metal stripes connected between them in the form of a matrix.
- Grid resistors are used as grounding resistors, brake resistors and harmonic filters for electric substations.

#### Water Resistors

- The construction includes tubes which carry saline solution with electrodes connected at both ends of the tube.
- The concentration of saline solution or salt water will determine the resistance.
- Because of the presence of water in the tubes, water resistors provide large heat capacity, which in turn result in high power dissipation.

#### SMD Power Resistors

Power resistors can also be made in the form of Surface Mounted Devices.

Because of their small size, the power dissipation capacity of SMD resistors is less than grid type resistors and water resistors.

Usually the power dissipated by SMD resistors is in the order of few Watts.

The range of power dissipated by different types of power resistors are as follows

- SMD Resistors 5 W or less
- Helical Wound 50 W or less
- Edge Wound 3.5 KW or less
- Grid Resistors 100 KW or less
- Water Resistors 500 KW or less

#### Applications of Power Resistors

Power resistors are used in applications where we need to dissipate large power. Some of the applications of Power resistors are

- Engine brakes in heavy locomotives and trams use power resistors. Locomotives move at high speed and possess high kinetic energy. While stopping these high speed locomotives, their kinetic energy is converted to heat.

Depending on the velocity of the locomotives, the amount of heat generated can be in the order of few Kilo Watts. Classic disc brakes can’t be used as they wear out easily. Hence regenerative brakes or high power resistors in the form of Grid resistors are used in locomotives. - Power resistors are used as grounding resistors to limit fault currents, high voltages and act as protective relays. These resistors can be rated up to 8 Kilo Amps.
- Power resistors are used as load resistors in turbines and Uninterruptible Power Supplies. They can be designed to provide adjustable resistance and can dissipate a power of up to 6 Mega Watts. Because of this high power dissipation, load resistors are equipped with an efficient cooling system to control the temperature and prevent the devices from burning out.

Prasad says

Its good basic knowledge od risister