Joule's law of Heating & Joules First Law

Edited By Vishal kumar | Updated on Jul 02, 2025 04:30 PM IST

As the electric current flows through the circuit, it increases the internal power of the conductor, resulting in the collision of electrons with the conductor atoms, which in turn leads to heat production. To measure the amount of heat transfer as a result of this collision, Joule, an English scientist, proposed Joule's law. In this article, we will study Joule’s Law of Heating and solve the numerical for better understanding.

This Story also Contains

Joule’s Law of Heating
Derivation of Joule's first law
Applications of Joule's Law
Solved Examples of Joule's law

Joule's law of Heating & Joules First Law

Joule’s Law of Heating

Joule's law explains the heat produced in a conductor and the factors affecting it. "The heat generated in the conductor due to the flow of electricity is directly proportional to the square of the current passing through it, the resistance of the conductor, and the time for which the current passes." Joule's law of heating is also termed as Joule's first law.

Joules law is mathematically represented by the following Equation

$$
H=I^2 R t
$$
Where:

$H=$ Heat produced (in joules)
$I=$ Current (in amperes)
$R=$ Resistance of the conductor (in ohms)
$t=$ Time (in seconds)

Joule's law is a mathematical interpretation of a scale in which resistance to a circuit converts electrical energy into thermal energy.

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Derivation of Joule's first law

When a current $I$ flows through a resistor $R$, the work done in time $t$ is given by:

$$
W=V I t
$$

where $V$ is the potential difference.

Using Ohm's law $V=I R$, the work done becomes:

$$
W=(I R) I t=I^2 R t
$$

The work done by the current in the resistor is entirely converted into heat energy (neglecting other losses). Thus:

$$
H=I^2 R t
$$

Explanation of Joule's law

To undertsand the concept of joule's law let's understand the terms associated with it in brief:

1. Current (I): Heat increases with the square of the current. If the current doubles, the heat increases fourfold.
2. Resistance (R): Higher resistance produces more heat for the same current and time.
3. Time (t): Heat is proportional to the duration of the current flow.

Applications of Joule's Law

Electric heaters: Heat is generated in devices like room heaters and electric kettles.
Fuses: Joule's law explains why fuses melt when excessive current flows through it.
Electric Bulb: The filament glows due to the heat generated by electric current.

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Solved Examples of Joule's law

Q1) Calculate the thermal energy produced to withstand $5 \Omega$ when the current 3 flows through it for 2 minutes.

Solution:

The temperature generated by the operator is given in the formula:

$$
H=I^2 R t
$$
$t=$ Time (in seconds) $=2$ minutes $=2 \times 60=120$ seconds

Substitute the values:

$$
\begin{gathered}
H=(3)^2 \times 5 \times 120 \\
H=9 \times 5 \times 120=5400 \text { joules }
\end{gathered}
$$

Q2) The $300 \Omega$ resistance heater is connected to the main feed for $\mathbf{3 0}$ minutes. If 10 current flows through a heater then what is the heat generated in the heater?

Solution:

The temperature generated by the heater is calculated as follows:

$\mathrm{H}=\mathrm{I}^2 \mathrm{RT}$

- $t=$ time ( 30 minutes $=30 \times 60=1800$ seconds)

Substitute the values

$$
H=(10)^2 \times 300 \times 1800
$$

$$
H=100 \times 300 \times 1800=54,000,000 or 54 \mathrm{~MJ}
$$

Frequently Asked Questions (FAQs)

1. What Is the Joule heating effects of Joules Heating Caused by Electric Current?

When electrical energy passes through the conductor, it increases the internal energy of the system, which in turn increases the energy of the atomic net and its molecules, which in turn leads to heat production. The heat generated in the system mainly depends on the major factors, namely

Electrical resistance provided by the operator is more resistance; there will be more heat to be produced.

The more current it flows, the more time it has, the more heat it produces.

The current value exceeds the driver. The higher the current size; heat is highly generated.

2. What are some other uses of Joules law?

1. Electric Heating Device

Other electrical appliances such as an electric heater, an electric toaster, and an electric heater are based on the current energy efficiency policy. In these applications, Nichrome (nickel alloy and chromium) is used as a heating element in many electrical devices. This is for the following reasons,

Nichrome has some high opposition.

Nichrome has a very melting point.

Nichrome is not easily integrated.

2. Fuse cable

Fuse cord is a mixture that contains 37% lead and 63% tin. Fuse cable is always connected to the series in the electrical circuit. With its high resistance to low melting point, when a large amount of electrical energy flows through the electrical circuit, the fuse wire melts, thus making the circuit open and preventing any damage to electrical equipment.

3. Electric Lamp

The power cord provides very high resistance to electrical flow, which is why a high temperature is produced. This cord, when intensified by incandescence, emits light. The most used cable is Tungsten, which has a high melting point of 3380 ° C.

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

Joules law of electric heating does not help even when the concept is used in systems such as transformers and dynamos. These are devices that help reduce energy loss due to the heat joule heating effect of electrical energy.

Other energy heating applications are:

Water heater

Incandescent lamp (when its cord is heated produces light).

Fuse (fuse melts and stops the flow of comments now in the region, reducing damage to home devices)

Electrical metal

Electric stove.

Thermistors: Thermistors are a type of resistance to their resistance when changes occur.

3. What About Joule vs. Watt?

Joule is a power unit of SI; it represents the amount of energy contained in the body. Watt is a measure of power conversion and is a unit of power SI.

Power = Time Power Time

Here unit Joule is equal to the value of a watt unit per second unit.

Watts = Joules / time

Energy is a measure of energy consumption per system.

1 Joule per second = 1 Watt

4. What is the significance of the Joule Act?

Joules law of temperature states that if the 'i' current passes through the resistor 'r' and the time 't' then the heat generated on the conductor is equal to the product of the square, the resistance at the same time.

5. What can Joules law predict?

Joules law, on electricity, is a mathematical definition of the rate at which circuit resistance converts electrical energy into thermal energy. ... You have found that the heat from a second equals the amount of electricity absorbed, or the loss of energy.

6. What is Joules law for burning section 10?

Joules law of temperature states that if the 'i' current passes through the resistor 'r' and time 't' then the heat generated in the conductor is equal to the product of the square square, the time resistance. H = i 2 rt.

7. Who got the Joule?

James Prescott Joule

James Prescott Joule, (born December 24, 1818, at Salford, Lancashire [now Greater Manchester], England - died October 11, 1889, Sale, Cheshire), an English scientist who discovered that different forces - mechanical, electrical, and thermal - alike is the same and can be changed to something else.

8. What is Joule's law of heating?

Joule's law of heating states that the amount of heat produced in a conductor is directly proportional to the square of the current flowing through it, the resistance of the conductor, and the time for which the current flows. It is expressed mathematically as H = I²Rt, where H is heat produced, I is current, R is resistance, and t is time.

9. How does Joule's law of heating differ from Joule's first law?

Joule's law of heating specifically relates to the heat produced in electrical conductors, while Joule's first law is a more general principle. Joule's first law states that the heat produced by a current is proportional to the work done by the current, regardless of the type of process involved.

10. How does resistance affect heat production according to Joule's law?

According to Joule's law, heat production is directly proportional to resistance. This means that doubling the resistance while keeping current and time constant will double the heat produced. This relationship explains why high-resistance materials are often used in heating elements.

11. Why does the heat produced depend on the square of the current in Joule's heating law?

The heat produced depends on the square of the current because the energy transferred to the electrons by the electric field is proportional to the current, and the rate at which these energetic electrons collide with the lattice (producing heat) is also proportional to the current. This double dependence results in the square relationship.

12. Can Joule's heating law be applied to all materials?

Joule's heating law applies to all conductors, but its effectiveness varies. It works best for materials with a constant resistance over the temperature range considered. For some materials, like semiconductors, the resistance changes significantly with temperature, making the law less accurate without additional considerations.

13. How does Joule heating affect the efficiency of electrical devices?

Joule heating often represents an undesired energy loss in electrical devices, reducing their efficiency. For example, in computers, Joule heating in processors necessitates cooling systems. However, in devices like electric heaters, Joule heating is the desired effect and contributes to efficiency.

14. What's the difference between Joule heating and induction heating?

Joule heating occurs due to current flowing through a resistive material, while induction heating is caused by eddy currents induced in a material by a changing magnetic field. Joule heating requires direct electrical contact, whereas induction heating can occur without contact, making it useful for heating conductive materials in sealed environments.

15. Can Joule heating be used beneficially in technology?

Yes, Joule heating has many beneficial applications. It's used in electric stoves, water heaters, space heaters, and incandescent light bulbs. In industry, it's used for processes like resistance welding. In medicine, it's utilized in electrosurgery and some forms of cancer treatment.

16. How does temperature affect Joule heating?

Temperature affects Joule heating in two ways. First, as temperature increases, the resistance of most conductors increases, leading to more heat production for the same current. Second, the rate of heat dissipation to the environment changes with temperature difference, affecting the net heating of the conductor.

17. Can Joule heating occur in semiconductors?

Yes, Joule heating can occur in semiconductors. However, the heating effect in semiconductors is more complex than in simple conductors because the resistance of semiconductors can change significantly with temperature and current. This can lead to non-linear heating effects and, in some cases, negative differential resistance.

18. What's the connection between Joule heating and the skin effect in conductors?

The skin effect, where alternating current tends to flow near the surface of a conductor, can influence Joule heating. At high frequencies, the effective resistance of the conductor increases due to the reduced cross-sectional area of current flow. This can lead to more intense heating near the surface of the conductor than would be expected from DC calculations.

19. Can Joule heating be used in energy harvesting?

While Joule heating is often considered a loss in electrical systems, it can be harnessed in certain energy harvesting applications. For example, thermoelectric generators use the Seebeck effect to convert temperature differences (which can be created by Joule heating) into electrical energy. However, the efficiency of such systems is generally low.

20. How does Joule heating relate to the concept of electrical power factor?

Joule heating is related to the power factor in AC circuits. The power factor is the ratio of real power (which produces Joule heating) to apparent power. A low power factor means that a significant portion of the current is not contributing to useful work or heating, but is still causing I²R losses in the transmission lines.

21. What's the relationship between Joule heating and electromigration in integrated circuits?

Joule heating exacerbates electromigration in integrated circuits. Electromigration is the transport of material caused by the gradual movement of ions in a conductor due to the momentum transfer between conducting electrons and diffusing metal atoms. The increased temperature from Joule heating accelerates this process, potentially leading to circuit failure.

22. Can Joule heating occur in electrolytes?

Yes, Joule heating can occur in electrolytes. When an electric current passes through an electrolyte, it encounters resistance, leading to heat generation. This principle is used in some electrochemical processes. However, in electrolytes, other effects like electrochemical reactions and ion movement also play significant roles in energy transfer.

23. What's the relationship between Joule heating and the photoelectric effect?

While Joule heating and the photoelectric effect are distinct phenomena, they can interact in certain scenarios. In photoemissive devices, Joule heating of the photocathode can affect its work function and thus its photoelectric properties. Additionally, in some photodetectors, Joule heating from the photocurrent can influence the device's sensitivity and noise characteristics.

24. Can Joule heating be used in medical treatments?

Yes, Joule heating has applications in medical treatments. It's used in electrosurgery, where high-frequency electrical currents heat and cut tissue. It's also employed in some cancer treatments, where carefully controlled heating of tumors (hyperthermia) can enhance the effectiveness of radiation or chemotherapy. Additionally, it's used in some forms of physical therapy to provide deep tissue heating.

25. How does Joule heating relate to the concept of electrical impedance?

In AC circuits, Joule heating is related to the real part of electrical impedance. While impedance includes both resistance and reactance, only the resistive component contributes to Joule heating. The heating

26. What's the relationship between Joule heating and energy conservation?

Joule heating demonstrates energy conservation. The electrical energy supplied to the conductor is converted into thermal energy (heat). No energy is created or destroyed; it's simply transformed from one form to another, aligning with the first law of thermodynamics.

27. How does Joule's law of heating relate to power dissipation in electrical circuits?

Joule's law of heating is directly related to power dissipation. The power dissipated in a resistor is given by P = I²R, which is the same as the rate of heat production in Joule's law (H/t = I²R). This shows that the electrical power is being converted to thermal power.

28. Why do power lines sag more on hot days, and how is this related to Joule heating?

Power lines sag more on hot days due to a combination of factors, including Joule heating. The current flowing through the lines generates heat (Joule heating), which is added to the ambient heat. This causes the metal to expand and the lines to lengthen, resulting in more sag. Higher resistance due to higher temperatures can exacerbate this effect.

29. Can Joule heating occur in superconductors?

In ideal superconductors, Joule heating does not occur. This is because superconductors have zero electrical resistance, and since Joule's law states that heat production is proportional to resistance, no heat is produced. However, in practical superconductors, some minimal heating can occur due to imperfections or under certain conditions.

30. How does the material of a conductor influence Joule heating?

The material of a conductor affects Joule heating through its resistivity. Materials with higher resistivity will produce more heat for the same current. Additionally, the temperature coefficient of resistance of the material determines how the heating effect changes as the conductor warms up.

31. How does Joule's law of heating apply to household electrical safety?

Joule's law is crucial for electrical safety. It explains why overloaded circuits or faulty wiring can lead to fires. As current increases (perhaps due to too many devices), heat production increases with the square of the current, potentially leading to dangerous temperatures if the wiring or circuit breakers are not properly rated.

32. How does Joule heating relate to the concept of electrical power?

Joule heating is directly related to electrical power. The power (P) dissipated in a resistor is given by P = I²R, which is identical to the rate of heat production in Joule's law (H/t = I²R). This shows that the electrical power input is being converted to thermal power output.

33. Why doesn't doubling the voltage across a resistor quadruple the heat produced?

Doubling the voltage doesn't quadruple the heat because of Ohm's law. When you double the voltage, the current doubles (V = IR). Since heat is proportional to I², doubling I leads to four times the heat. However, this is exactly balanced by the doubling of V, so the heat production only doubles, not quadruples.

34. How does Joule heating in transmission lines affect power distribution efficiency?

Joule heating in transmission lines reduces power distribution efficiency. As electricity flows through the lines, some energy is lost as heat due to the lines' resistance. This loss increases with distance and current, which is why high-voltage transmission is used for long distances to reduce current and minimize losses.

35. Can Joule heating occur in alternating current (AC) circuits?

Yes, Joule heating occurs in AC circuits. The heating effect depends on the root mean square (RMS) value of the current, not its instantaneous value. The formula becomes H = I²RMS Rt, where IRMS is the root mean square current.

36. How does the cross-sectional area of a wire affect Joule heating?

The cross-sectional area of a wire inversely affects Joule heating. A larger cross-sectional area reduces the resistance of the wire (R = ρL/A, where ρ is resistivity, L is length, and A is area). Lower resistance means less heat production for the same current, according to Joule's law.

37. What's the relationship between Joule heating and the drift velocity of electrons?

Joule heating is related to the drift velocity of electrons. As electrons move through a conductor, they collide with atoms, transferring kinetic energy which becomes heat. The drift velocity determines the rate of these collisions. Higher drift velocity (higher current) leads to more collisions and more heat production, aligning with Joule's law.

38. How does Joule heating relate to the concept of electrical resistance?

Joule heating is directly proportional to electrical resistance. This relationship exists because resistance is a measure of how much a material opposes the flow of electric current. The energy lost in overcoming this opposition is converted to heat. Materials with higher resistance produce more heat for the same current.

39. Can Joule heating occur in a perfect conductor?

In a theoretically perfect conductor with zero resistance, Joule heating would not occur. This is because Joule's law states that heat production is proportional to resistance (H = I²Rt). If R = 0, then H = 0 regardless of the current. However, perfect conductors don't exist in reality; even superconductors have some minimal resistance under certain conditions.

40. What's the connection between Joule heating and the Second Law of Thermodynamics?

Joule heating is a manifestation of the Second Law of Thermodynamics. It represents the irreversible conversion of ordered energy (electrical) into disordered energy (heat), increasing the entropy of the system. This process is spontaneous and cannot be reversed without external work, aligning with the Second Law.

41. How does Joule heating relate to the concept of electrical energy?

Joule heating represents the conversion of electrical energy to thermal energy. The electrical energy supplied to a circuit (E = VIt) is equal to the heat energy produced (H = I²Rt) when all the energy is dissipated as heat. This equivalence demonstrates the conservation of energy principle.

42. Why is Joule heating sometimes called "resistive heating"?

Joule heating is often called "resistive heating" because it occurs due to the electrical resistance of a conductor. The term emphasizes that the heating effect is a result of the material's resistance to the flow of electric current, distinguishing it from other forms of electrical heating like induction heating.

43. How does Joule's law of heating apply to the design of fuses?

Joule's law is crucial in fuse design. Fuses are safety devices that intentionally heat up and melt when the current exceeds a safe level. The fuse wire is designed with a specific resistance and melting point, so that the Joule heating effect will cause it to melt and break the circuit at the desired current level.

44. How does Joule heating relate to the concept of electric field?

Joule heating is related to the electric field within a conductor. The electric field accelerates charge carriers (usually electrons), increasing their kinetic energy. As these energetic charge carriers collide with the lattice, they transfer this energy, which manifests as heat. The stronger the electric field, the greater the energy transfer and thus the heating effect.

45. What's the relationship between Joule heating and the length of a conductor?

The length of a conductor affects Joule heating through its influence on resistance. The resistance of a wire is directly proportional to its length (R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area). Therefore, doubling the length of a wire doubles its resistance and, according to Joule's law, doubles the heat produced for the same current.

46. How does Joule's law of heating apply to the design of heating elements?

Joule's law is fundamental in designing heating elements. Engineers use the law to calculate the resistance needed to produce a desired amount of heat for a given current. They also consider factors like the material's temperature coefficient of resistance and melting point to ensure the element can operate safely and efficiently at high temperatures.

47. Can Joule heating be used to measure electrical current?

Yes, Joule heating can be used to measure electrical current in devices called hot-wire ammeters. These instruments contain a wire that heats up due to the current passing through it. The expansion of the wire moves a pointer on a scale. The amount of expansion, and thus the pointer's position, is related to the current by Joule's law.

48. How does Joule heating in electrical contacts affect their performance?

Joule heating in electrical contacts can significantly affect their performance. As contacts heat up, their resistance may increase, leading to more heating. This can cause oxidation, melting, or welding of the contacts, potentially leading to failure. Proper contact design and material selection are crucial to manage this heating effect and ensure reliable operation.

49. How does Joule's law of heating apply to lightning strikes?

Joule's law explains the intense heating effects of lightning strikes. The extremely high current in a lightning bolt, even for a very short duration, produces enormous amounts of heat according to the I²Rt relationship. This heat is responsible for the damage caused by lightning, including the vaporization of materials and the ignition of fires.

50. How does Joule's law of heating apply to the phenomenon of electrical breakdown?

Joule's law plays a role in electrical breakdown. As the voltage across an insulator increases, any small current that begins to flow can cause Joule heating. This heating can create a positive feedback loop: heating reduces the material's resistance, allowing more current to flow, causing more heating. This process can lead to rapid breakdown of the insulator.

51. How does Joule heating in supercapacitors affect their performance?

Joule heating in supercapacitors can significantly impact their performance. During rapid charging or discharging, the high currents can cause substantial heating. This can lead to increased self-discharge rates, reduced cycle life, and in extreme cases, safety issues. Managing this heat through proper design and materials selection is crucial for supercapacitor performance and longevity.

52. How does Joule's law of heating apply to the design of circuit breakers?

Joule's law is fundamental in circuit breaker design. Circuit breakers use a bimetallic strip that bends when heated by the current passing through it. The strip is designed so that at a specific current (determined by Joule heating), it bends enough to trip the breaker. This allows the breaker to respond to both sudden high currents and prolonged moderate overcurrents.