 # Joule's Law

### Introduction

Sir James Prescott Joule formulated Joules law. It establishes a relationship between heat, voltage, current, and time.

When an electric current passes through a circuit or a conductor, heat is produced. This is due to the collision of electrons. So, what is the amount of heat that is generated due to the flow of current through a wire? What is the concept behind heat generation? What are the parameters, and what are the hindrances to heat generation? The law of heating that answers all these questions is given by Joules Law.

### Joule's Law Definition

When an electric current flows through a circuit, it increases the internal energy of the conductor, which gives rise to the collision of electrons with atoms of the conductor, and which results in heat generation. To measure the amount of heat generated due to these collisions, Joule, an English physicist, gave the Joule's law.

Joule's law, when an electric current passes through a conductor, heat H is produced, which is directly proportional to the resistance R of the conductor, the time t for which the current flows, and to the square of the magnitude of current I. Mathematically it is represented as H ∝ I² .Rt.

### Joule’s Law of Heating Equation

Joule's Law is Represented Mathematically by the Following Equation

1. The heat produced in a conductor due to the flow of electric current through it varies directly as the square of the magnitude of current when the resistance offered by the conductor and the time of flow of electrical current is constant.

H ∝ i²

i.e H ∝ i² [When R and t are constant]

1. The amount of heat produced in a conductor due to the flow of electric current through it is directly proportional to the resistance offered by the conductor when the time of flow and the magnitude of the current is constant.

i.e H ∝ R [When i and t are constant]

1. The heat produced in a conductor due to the flow of current is directly proportional to the time duration of current flow when the electrical resistance and the magnitude of current are constant.

i.e H ∝ t [When i and t are constant]

If these three conditions are merged, the resulting generalized formula is given by

H ∝ i².R.t[When i, R and t all are variable]

H = $\frac{1}{J}$.i².R.t [∵ J is a Joule constant]

Where H is the heat produced, and its SI unit is Joule, i is the current flowing in the conductor, t is the time of current flow, and J is a proportionality constant known as Joule's mechanical equivalent of heat.

The mechanical equivalent of heat is defined as the number of units of work that must be done to a system to produce a heat of unit quantity. The value of the mechanical equivalent of heat depends on the value of the work done to the system and the heat produced by it. It has been experimentally found that J = 4.2 joules/cal ( and 1 joule = 107 ergs) = 1400 ft. lbs./CHU = 778 ft. lbs/B Th U. These values give precise values, much accurate to the real values during experiments of heat calculations.

1. What are the Joules Heating Effects Caused by Electric Current?

When an electric current passes through a conductor, it increases the internal energy of the system, which in turn increases the net energy of its constituent atoms and molecules, finally resulting in the production of heat. The heat produced in a system mainly depends on a major of factors, which are

• The electrical resistance offered by the conductor more is the resistance; more will be the heat produced.

• The time for which the current flows, more is the time duration, more is the heat generated.

• The amount of current that passes through the conductor. Higher is the magnitude of current; more is the heat produced.

2. What are Some Applications of Joule's Law?

1. Electric Heating Device

Some electrical devices like electric iron, electric toaster, and electric heater are based on the principle of heating effect of electric current. In these devices, Nichrome (an alloy of nickel and chromium) is used as a heating element in many electrical devices. This is because of the following reasons,

• Nichrome has high specific resistance.

• Nichrome has a high melting point.

• Nichrome is not oxidized easily.

2. Fuse Wire

Fuse wire is an alloy which contains 37% lead and 63% tin. Fuse wire is always connected in series in electric circuits. As it has high resistance and low melting point, when a large magnitude of electric current flows through the electric circuit, the fuse wire melts, thereby making the circuit open and preventing any damage to the electrical devices.

3. Electric Bulb

The filament of an electric bulb offers very high resistance to the flow of electric current, that's why a high amount of heat is produced. This filament, when heated to incandescence, emits light. Normally used filament is Tungsten, which has a very high melting point of 3380°C. The filament of an electric bulb is enclosed in a glass that contains an inert gas at low pressure.

Electric arc and electric welding are also based on the heating effect of electrical current.

Joule's law heating effect of electric current is not useful when the concept is applied to systems like transformers and dynamos. These are the devices that help to reduce the loss of energy due to the heating effect of electric current.

Some more applications of heating effect of electric current are:

• Water heater

• The incandescent bulb (when its filament is heated it generates light).

• Fuse (the fuse melts down and stops toe current flow in the circuit, minimizing the damage to the household devices)

• Electric iron

• Electric stove.

• Thermistors: Thermistors are a kind of resistors whose resistance changes when there is a change in temperature.

3. What About a Joule vs. a Watt?

Joule is the SI unit of energy; it represents the amount of energy contained in the body. Watt is the rate of change of energy, and it is the SI unit of power.

Energy=Power ∗ Time

Here the unit Joule is equivalent to a unit amount of watt for a unit second.

Watts = Joules / time

Power is the rate of consumption of energy by a system.

1 Joule per second = 1 Watt

1 Joule per millisecond = 1000 Watt = 1 kW (kilowatt)

1 Joule per microsecond = 1000000 W = 1 MW (megawatt).