Heating Effect of Current and Electric Fuse: Class 10

Quick answer: When current flows through a resistor, electrical energy is converted into heat. By Joule's law of heating, the heat produced is $H = I^2Rt$: it is proportional to the square of the current, the resistance and the time. Heating elements use alloys such as nichrome because they have high resistivity and do not oxidise easily when hot. A fuse is a wire of suitable melting point placed in series with the device; if the current becomes too large, it melts and breaks the circuit. A 1 kW iron at 220 V draws about 4.5 A, so it needs a 5 A fuse.

Why current produces heat

A battery or the mains supply does work to keep charge flowing through a resistor. Part of this energy may do useful work (for example, turning a fan), but in a pure resistor all of it is converted into heat. This is the heating effect of electric current.

Joule's law of heating

Step 1: The work done in moving charge $Q$ through a potential difference $V$ is $W = VQ$.

Step 2: Since $Q = It$, the work done in time $t$ is $W = VIt$.

Step 3: By Ohm's law, $V = IR$, so

$H = W = I^2Rt$

This heat is in joules when $I$ is in amperes, $R$ in ohms and $t$ in seconds.

The heat produced is:

• proportional to the square of the current for a given resistance,
• proportional to the resistance for a given current,
• proportional to the time for which the current flows.

Example: A 100 Ω resistor carries 2 A for 10 s. Then $H = 2^2 \times 100 \times 10 = 4000$ J.

Uses of the heating effect

The resistivity of nichrome is roughly 60 times that of copper, so a short length of nichrome gives a large resistance and produces a lot of heat.

The electric fuse

A fuse protects circuits and appliances from too much current.

Step 1: The fuse wire is connected in series with the appliance, in the live wire.

Step 2: If the current rises above the safe value (because of a short circuit or overloading), the heat $I^2Rt$ in the fuse wire raises its temperature.

Step 3: The fuse wire melts and breaks the circuit, stopping the current before the wiring or the appliance is damaged.

Because the fuse is in the live wire, a blown fuse disconnects the appliance from the high-voltage side of the supply. Fuses used at home are commonly rated 1 A, 2 A, 3 A, 5 A and 10 A.

Choosing a fuse rating

An electric iron uses 1 kW at 220 V. What fuse should be used?

Step 1: Find the normal current: $I = \frac{P}{V} = \frac{1000}{220} \approx 4.54$ A.

Step 2: The fuse rating must be a little higher than this, so that the fuse does not blow during normal use.

Answer: A 5 A fuse should be used.

Summary table

Exam tips

• Learn the derivation of $H = I^2Rt$ from $W = VQ$; it is a common short-answer question.
• In fuse questions, find $I = \frac{P}{V}$ first, then choose the next standard rating above it.
• State that heat depends on $I^2$, so doubling the current gives four times the heat.

Common mistakes

• Writing $H = IRt$ and forgetting the square on the current.
• Using a thick copper wire as a fuse. It has a high melting point and low resistance, so it will not melt in time.
• Connecting the fuse in parallel. It must be in series to break the circuit.
• Choosing a fuse rated below the normal working current, which would blow during normal use.

Frequently Asked Questions

What is Joule's law of heating?

The heat produced in a resistor is H = I²Rt: proportional to the square of the current, the resistance and the time.

Why are alloys used in electric heating devices?

Alloys such as nichrome have high resistivity and do not oxidise (burn) easily at high temperatures.

Why is tungsten used for bulb filaments?

Tungsten has a very high melting point (3380 °C), so it can glow white-hot without melting.

How does an electric fuse work?

When the current becomes too large, the fuse wire heats up and melts, which breaks the circuit and stops the current.

What fuse should be used for a 1 kW iron at 220 V?

The current is about 4.54 A, so a 5 A fuse should be used.