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# Joule's Law of Electric Heating

### Key Takeaways

• According to Joule’s law of electric heating, the amount of heat generated is proportional to the resistance of the wire, the time duration for which the current flows, and the square of the current flowing through the circuit.

• When the same current is passed through different resistors for the same time duration, the heat generated is proportional to the resistance value.

• When an excessive current flows through the circuit due to Joule heating, the fuse wire melts and disconnects the circuit from the supply. Fuse wire is a protection method used in electric circuits to isolate critical sections during high circuit flow

Heat is a spin-off of electric current flow, which is the flow and collision of electrons  that results in heat generation. Joule’s law of electric heating introduces the mathematical equation that describes how much heat is generated due to the flow of current. We will discuss the heating impact of electric current, Joule's law, and heating applications of electric current in this article.

## Joule’s Law of Electric Heating

English physicist James Prescott Joule conducted an experiment by immersing a length of wire in a known mass of water and recorded the temperature rise by allowing a known current to flow through the wire for half an hour. By conducting the experiment for different lengths of wire and current, he established a relationship between heat generation and current amplitude through the wire. The results from the experiment were first published in the proceedings of the Royal Society and later became known as Joule’s law of electric heating.

According to Joule’s law, the amount of heat generated is proportional to the resistance of the wire, the time duration for which the current flows, and the square of the current flowing through the circuit. The mathematical equation explaining Joule’s law of electric heating can be given by:

### Q = I2  Rt

Q is the amount of heat generated in Joules.

I is the amplitude of the current flowing through the wire.

R is the resistance of the wire.

t is the time in seconds for which the current flows through the wire.

 Fun Fact: The unit of heat, Joule, is named after the famous English physicist, James Prescott Joule.

## Joule’s Law Interpretations

From the equation above, it is clear that the heat generated is dependent on the current flowing through the wire, time, and resistance. The law can be interpreted mathematically under conditions where some parameters are constant.

### Resistance and Time Are Constants

The current through the wire is varied, and the resistance of the wire and the time for which the current is passed is kept constant. The heat generated is proportional to the square of the current.

Q α  I2

### Resistance and Current Are Constant

The time for which the current flows through a wire is varied, keeping the resistance of the wire and current constant. The amount of heat generated becomes proportional to time.

Q  α  t

### Current and Time Are Constant

When the same current is passed through different resistors for the same time duration, the heat generated is proportional to the resistance value.

Q α  R

## Joule’s Equivalent of Electrical Energy

Heating is associated with loss in electric circuits. Imagine current passing through a resistor and the body of the resistor heating up. The heat generated is the loss of energy and is usually called heating loss or I2Rt loss.

With Joule's law of electric heating equation, we can determine the Joule equivalent of electrical energy. However, we know that energy is the product of power and time. Hence, the energy generated in Joules can be equated to a watt second.

1 watt-second = 1 Joule

One unit of energy is 1 kW hr. Converting the left-hand side of the above equation to 1 unit.

103×60×60 watt second = 103×60×60 J

1 kWhr = 3600×103J

 1 kWhr = 3.6×106J  One unit of electricity is equivalent to 3.6×106J of heat

## Joule’s Heating Effect Applications

Electric kettles, heaters, geysers, toasters, and iron boxes are just some of the daily applications of Joule’s heat effect.

### Incandescent Bulbs

In electric bulbs, a high-resistance filament, usually made of tungsten, is used. As current flows through the filament, it produces high heat. As the melting point of tungsten is very high, it withstands heat. However, light is emitted due to the heating effect. In incandescent lamps, more power is lost in the form of heat, and with the emergence of LEDs, there is a rapid decline in usage.

### Fuse Wire

Fuse wire is a protection method used in electric circuits to isolate critical sections during high circuit flow. Usually, the fuse wires form a series connection with the supply and the circuit. The wires are made of materials with high resistance and a low melting point.

When an excessive current flows through the circuit due to Joule heating, the fuse wire melts and disconnects the circuit from the supply. The critical sections of electric circuits are protected from short circuits by fuse wire. Usually, the alloy of tin and lead is used as fuse wire.

## Applying Joule’s Law of Electric Heating

Using Joule’s law of electric heating equation, it is possible to determine what time a fuse wire will disconnect the circuit or what resistance of a wire is required to disconnect the circuit within a given time when a definite value of current flows through the circuit. When any combination of two of the three parameters in the Joule heating formula (current, resistance, and time) are constant, the heat generated is proportional to the third parameter, which varies.

With the help of Cadence AWR software, you can design applications that intentionally make use of Joule heating as well as reduce the power losses due to heating in electrical systems. Cadence Celsius Thermal Solver helps in analyzing the thermal model of electronic systems and saves you time.

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