Chapter 11 · Question 9

State Joule's law of heating. Explain two practical applications of the heating effect of electric current.

Answer Revealed

Direct Answer:

Joule's law of heating states that the heat

H

produced in a resistor is (i) directly proportional to the square of the current (

H \propto I^2

), (ii) directly proportional to the resistance (

H \propto R

), and (iii) directly proportional to the time for which the current flows (

H \propto t

). Therefore,

H = I^2 R t

. Applications include: (1) Electric fuse — a thin wire of low melting point melts and breaks the circuit when current exceeds a safe limit, protecting appliances. (2) Heating elements in devices like electric iron and geyser — made of alloys like nichrome which have high resistivity and high melting point, so they produce large amounts of heat without melting.

Simple Explanation

Joule's law says the heat produced by a current depends on how much current flows, the resistance of the material, and how long it flows — heat goes up with the square of the current. This is used in fuses (thin wire that melts if too much current passes, breaking the circuit for safety) and in heater coils (nichrome wire that glows red-hot in irons, toasters, and room heaters because it has high resistance).

Exam-Ready Structure

Joule's law of heating quantitatively describes the conversion of electrical energy into heat energy in a resistive circuit: 1. Joule's law statement: The heat produced in a resistor (

H

) is (i) directly proportional to the square of current for a given resistance and time (

H \propto I^2

), (ii) directly proportional to the resistance for a given current and time (

H \propto R

), (iii) directly proportional to the time for which the current flows through the resistor (

H \propto t

). Mathematically,

H = I^2 R t

. This can also be expressed as

H = V I t

H = (V^2 / R) t

using Ohm's law. 2. Application 1 — Electric fuse: A fuse wire is a thin, short piece of wire made of an alloy with low melting point (like tin-lead alloy). It is connected in series with the live wire in a circuit. When the current exceeds the rated safe value, the fuse wire heats up (

H = I^2 R t

) and melts, breaking the circuit and preventing damage to appliances. The fuse rating (in amperes) is chosen based on the circuit's maximum safe current. 3. Application 2 — Heating elements: Devices like electric iron, electric heater, geyser, and toaster use heating elements made of high-resistivity alloys (typically nichrome — an alloy of nickel, chromium, iron, and sometimes manganese). Nichrome is chosen because: (a) it has high resistivity, so it produces significant heat, (b) it does not oxidise easily at high temperatures, and (c) it has a high melting point, allowing it to become red-hot without melting. The filament of an electric bulb is also a heating application — it is made of tungsten which has a very high melting point and becomes white-hot to produce light. 4. The heating effect is both useful (in the above applications) and a source of energy loss in transmission lines and appliances, which is why efforts are made to minimise it where heat is not desired.

Key Points

Joule's law: $H = I^2 R t$ (heat proportional to $I^2$ , $R$ , and $t$ )
Electric fuse: thin wire of low melting point melts at excess current, protecting the circuit
Heating elements: made of nichrome alloy (high resistivity, high melting point, oxidation-resistant)
Electric bulb filament: tungsten wire with very high melting point, becomes white-hot
Heating effect is useful in appliances but undesirable in transmission lines

State Joule's law of heating. Explain two practical applications of the heating effect of electric current.