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Joule's Law

Last updated date: 27th May 2024
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What is Joule’s Law?

The amount of heat that is produced within an electric wire due to the flow of current is expressed in the unit of Joules. When the current flows through the wire there is a collision between electrons and atoms of the wire which leads to the generation of heat. Joule’s Law states that when a current flows in a conductor the amount of heat generated is proportional to current, resistance, and time in the current flowing. Let us have a look at the concept behind the joule’s law.

Mathematical Representation of Joule’s Law

  1. When in a current conducting wire the time of the flowing of current and the resistance of the wire is constant, the amount of heat produced and the square of the amount of current flowing the wire are proportional to each other.

Equation 1 :  \[H \alpha i^{2}\] (Where R and T are Constant)

  1. When in a current conducting wire the time of the flowing of current and the current of the wire are constant, the amount of heat produced and the amount of electrical resistance of the wire are proportional to each other.

Equation 2: \[H \alpha R\] (Where R and T are Constant)

  1. When in a current conducting wire the amount of the electrical resistance and the amount of current are constant, the heat produced and the time of current flowing are proportional to each other.

Equation 3: \[H \alpha t\] (Where R and i are Constant)

Formula of Heat

When equations 1, 2, and 3 are merged, the resulting formula is-

\[H \alpha i^{2}. Rt\] (i, R, and t are variables)

\[H = \frac{1}{J}.i^{2}RT\]  (where J is a Joule’s Constant)

The joule’s constant J is defined as the number of work units that furnishes one unit of heat when converted completely into heat. 

The value of J= 4.2 joules/cal.

\[H = \frac{1}{J}.i^{2}RT\] 

\[H = \frac{i^{2}Rt Joules}{\frac{4.2 Joules}{cal}}\]  

= \[ \frac{i^{2}Rt}{4.2 Joules}\]

= \[ \frac{i^{2}Rt}{4.2 Joules}\]

= \[0.24 i^{2} Rt cal\]

According to Joule’s law 

\[I^{2} Rt\] = work done in joules when through a resistor of R ohmsi Ampere of current is maintained for t seconds.

\[H = 0.24 Vit cal = 0.24\frac{v^{2}}{R}cal (V = iR)\]

Electrical Power

The rate at which the work is done in an electric circuit in order to maintain the steady current is known as the electrical power of that circuit. It can also be stated as the rate at which the electrical energy is converted into other forms of energy. The SI unit of electrical power in watts W.

\[P = \frac{w}{t} = \frac{I^{2}Rt}{t}\]

\[P = I^{2}R = IV = \frac{V^{2}}{R}\]

FAQs on Joule's Law

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 is more is the resistance; more will be the heat produced.

  • The more time for which the current flows, more is the more time duration, more is the more 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?

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.

Fuse Wire: Fuse wire is an alloy that 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.

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. The 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 the 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).

4. What is electric energy and what is its formula?

The total work done in an electric circuit in order to maintain the current is known as electrical energy. The electric energy in mathematical terms-

Electrical energy = W = V I t = P t

Electrical energy = electric power * time

The SI unit of electrical energy is Joule, J and is measured in kWh (kilowatt-hour) in practice.

Electrical energy in kW = Power in kW * Time in hours

1 kWh is one unit of electrical energy. Therefore, if we say that a consumer has consumed 50 units that means that the electrical energy consumption is 100 kWh.

5. What are the practical applications of Joule’s law?

The practical applications of Joule’s law include various applications in transportation, home, and industry. Joule’s law is applied on the incandescent light bulbs where light is emitted when the filament is heated with electricity. Resistance ovens are another example of Joule’s Law where the heat is put through convection and radiation from the conductor. Different types of ovens where joule’s law is used are toaster ovens, home oven broilers, and industrial electric ovens. Resistance direct heating is used in heat stoves, bread toasters, car windshields, office coffee makers. While induction heating is used in industrial induction ovens and induction stoves.

6. What is the drawback of Joule’s Law?

The main downside of Joule’s effect is the energy that is lost when it is transformed into heat and when the electrical appliances are overheated. Joule’s law is undesirable in many applications for the reason that some electronic devices need a heat sink in order to avoid the excessive heating of the various components and devices. Part of electric power is dissipated as heat when it is converted into thermal energy. This is the reason why the heat that is produced is a form of wasted energy.

7. What is the reason behind the transmission of energy over high voltage lines?

The overhead power lines are used to transfer the electrical energy from producers to consumers. There is 0 resistance in these power lines which causes transmission losses. In order to minimize these transmission losses, there are two solutions- 

  • The first step is to reduce the resistance of the conductors. With the use of copper conductors, the line resistance is reduced.

  • According to ohm’s law, to lower the current intensity, increase the voltage. This will decrease the number of electrons circulating through the conductor and hence the collisions are reduced.

8. What is Ohm’s law?

Ohm’s Law states that when all the physical conditions and temperature are constant, the voltage across a conductor and the current flowing through it are proportional to each other.  The current-voltage relationship can be written in mathematical terms as V=IR. The unit of resistance is ohms and is denoted by the symbol. In the cases where the temperature is raised and the current is increased, ohm’s law cannot be applied.