# What is Joule’s Law and Heating Effect of Current

**Joule’s Law – Joule Effect or Heating Effect of Current and its Applications**

An English physicist James Prescott Joule discovered the Joules’ law (also known as Joel’s effect, Joule-Lenz law or Joule’s first law) in 1840-43 which shows the relation between current, heat and resistance in a specific time i.e. when a current flows through a material, it produces heat in it.

Table of Contents

**Joule’s Law**

**Joule’s Law** states that “If “I” amperes current flows through a resistor “R” for “t” seconds, then the amount of work done (conversion of electrical energy into heat energy) is equals to

**Work done = Heat = I ^{2}Rt … Joules**

or

WD = Heat = VIt … Joules … (∴ R = V/I)

or

WD = Heat = Wt … Joules … (∴ W = VI)

or

WD = Heat = V^{2}t/R … Joules … (∴ I = V/R)

The work done is the amount of heat energy converted from electricity which dissipates in the air. In this case, the produced amount of heat can be calculated using the following formulas and equations.

**Amount of Heat produced = H = Work done / Mechanical equivalent of Heat = WD/J**

Where:

- J = 4187 joules/kcal = 4200 joules/kcal (approx.)
- ∴ H = I
^{2}Rt / 4200 kcal = VIt / 4200 kcal = Wt / 4200 kcal = V^{2}t / 4200 kcal

A one kilocalorie (kcal) is the amount of heat needed to rise the temperature of one kilogram (kg) water by one degree centigrade (1°C).

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### Heating Effect of Current

Almost, we all have experienced that when a current flows through a conductor or cable and wire, it becomes hot later. The reason behind this scene is that when current flows through a conductor, the applied electrical energy is converted into heat energy which increases the temperature of the conductor.

We know that the flow of electrons in a substance is known as electric current. The drifting electrons in the substance collides with each other and the electrons of molecule atoms in the material. The collision of electrons produces heat. That’s the reason why the flowing of electric current in a substance generates heat. This effect is known as the heating effect of the current.

The generated heat by electric current depends on the amount of current and material of that substance. For example,

Electric current produces more heat in insulators (those materials which heavily oppose the flow of current in it e.g. tungsten, nichrome) while the amount of heat generated by flowing current in conductors (those material in which current flows very easily due to less or almost negligible resistance e.g. gold, copper, aluminum) is less than that of insulators).

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### Why does the element of the heater glow due to heat but not the heater’s cord?

Generally, the heating element of heaters are made up of nichrome which has very high resistance. When a supply voltage is applied across the heating element through the wire, the material heavily opposes the flow of electrons in it. Due to the drifting of electrons inside the heating material, the electrons collide with the electrons in the material atoms. This continuous collision of electrons heats up and glows the heating element which additionally provides the heat energy. In simple words, the heating element of nichrome converts the electrical energy into heating energy. This whole process is known as the heating effect of current.

On the other hand, the cord wire connected to the heater is made of conductor where current easily flows through it without a noticeable resistance. That’s why only the heater element glows, but not the heater’s cable.

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### Solved Example on Joule’s Law of Heating Effect of Current

**Example:**

An electric heater contains 1.6kg of water at 20°C. It takes 12 minutes to rise the temperature to 100°C. Assume the losses due to radiation and heating the kettle to be 10kg-calories. Find the power rating of the heater.

**Solution**

Heat required to rise the temperature of 1.6kg of water to boiling point = 1.6 x 100 x 1 x (100 – 20) cal.

= 128000 cal.

Heat lost = 10 x 1000 = 10000 cal.

Total heat = 128000) + 10000 = 138000 cal.

Now, heat produced = Wt = (W x 12 x 60) / 4.2 cal.

Heat produced = heat taken by heater i.e.

= (W x 12 x 60)/4.2 = 138000

W = (138000 x 4.2) / )12 x 60)

**W = 805W = 0.8kW**

### Applications of Joule’s Effect or Heating Effect of Current

Joule’s law or heating effect of electric current are used in many household and industrial applications. Following are the appliances and devices using the effect of electric current.

- Electric heaters, stoves, water heaters and heating elements
- Electric clothes iron
- Electric hot plate
- Electric Welding
- Food processing
- Filament of Incandescent lamps and light bulbs
- IR Thermal imaging (Infrared thermography (IRT) of a light bulb
- Resistance heating coils, space heater (electric radiator), immersion heaters PTC heaters, cartridge heaters, and fan heaters
- Hair dryers
- Soldering iron
- Fuses and fuse elements

Besides these useful applications of heating effect of current, there are some drawbacks as well such as electric power loss (I^{2}R) in the HVAC (high voltage alternating current) power and transmission lines due to the fact that there is some resistance of the power lines material. Moreover, it leads to serious heating problem in electrical machines and devices such as transformer, generator and motors etc.

Additionally, The thermal efficiency or heating efficiency of current can’t be used at all because there are some heating losses due to the radiation (transfer of the heat in the form of heating waves) and convection (the molecular movement in the material used to transfer the heat).

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