9. Heating Effect of Electric Current

Joule's Law of Heating

When electric current flows through a conductor that has resistance, some of the electrical energy is converted into heat energy because of collisions between the moving charge carriers and the atoms of the conductor. This is called the heating effect of current, and the quantitative law governing it was established by James Prescott Joule and is known as Joule's law of heating. It states that the heat produced in a conductor is directly proportional to the square of the current, directly proportional to the resistance, and directly proportional to the time for which the current flows:

H = I² R t

Here H is the heat produced (in joules, when I is in amperes, R in ohms, and t in seconds). Notice that heat depends on the square of the current, so doubling the current quadruples the heat generated in the same time — a fact often tested in numerical questions.

Applications of the Heating Effect

• Electric heater / electric iron / room heater / immersion rod / toaster: These appliances use a coil of high-resistance wire, typically made of nichrome (a nickel-chromium alloy), through which current is passed. Nichrome is chosen because it has high resistivity (so it heats up strongly for a modest current) and a very high melting point together with resistance to oxidation, so it can glow red-hot repeatedly without burning out or reacting with air.
• Incandescent electric bulb: A thin tungsten filament is heated to incandescence (white heat, around 2500–3000°C) by the passage of current through its high resistance, causing it to emit visible light. Tungsten is chosen for its extremely high melting point (about 3380°C) and low rate of evaporation at high temperature. The filament is housed in a glass bulb filled with an inert gas (commonly argon or nitrogen) to prevent the tungsten from burning up in air (oxidising) at such high temperatures.
• Electric fuse: A fuse is a short length of thin wire made of a metal or alloy (typically an alloy of tin and lead, or sometimes copper) with a low melting point and a resistance high enough to heat up appreciably when carrying current. A fuse is connected in series in the live wire of a circuit, and is deliberately rated to carry a certain maximum safe current. If the current exceeds this rated value — for example, due to a short circuit or a sudden overload — the fuse wire heats up rapidly (by Joule's law) and melts, breaking the circuit before the excess current can damage the appliance, overheat the wiring, or start a fire. The fuse is thus a vital safety device; it must always be connected to the live wire (never to the neutral wire alone), so that when it blows, the appliance is fully disconnected from the supply.
• Electric arc welding and soldering irons also make direct use of the heating effect of current.