Heating Effect of Electric Current

When electric current passes through a conductor, charge carriers move through the material. During their motion, they collide with the particles of the conductor, and a part of the electrical energy is converted into heat energy. As a result, the conductor becomes hot. This phenomenon is called the heating effect of electric current.

Electric heaters, electric irons and many other heat-producing electrical appliances work on this effect.

Joule's Law of Heating

Joule's law of heating can be explained using three proportional relationships.

1. Effect of Current

When resistance and time remain constant — H ∝ I² ---(i)

2. Effect of Resistance

When current and time remain constant — H ∝ R ---(ii)

3. Effect of Time

When current and resistance remain constant — H ∝ t ---(iii)

Using the rule of combined variation from equations (i), (ii) and (iii), we get

— H ∝ I²Rt

or,

where J is a constant called the mechanical equivalent of heat. Its value is 4.2 J/cal.

This is a form of Joule's heating law used when heat is calculated in calories.

📚 When heat is measured in joules, H = I²Rt

📚 When heat is measured in cal, = 0.24 I²Rt

Using Ohm's law V = IR, we get two more useful forms —

and,

In calories, approximately —

👉 Important Results of Heat Production

• For the same R and t, if current is doubled, the heat produced becomes four times.
• For the same I and t, if resistance is doubled, the heat produced doubles.
• For the same I and R, if time is doubled, the heat produced doubles.
• For the same resistance and time, increasing potential difference gives .

👉 Electrical Energy

When a charge Q is moved through a potential difference V, the electrical energy involved is —

Since Q = It,

Using Ohm's law,

and,

In resistive appliances, a large part of this electrical energy may be converted into heat.

👉 Electrical Power

The rate at which electrical energy is used with respect to time is called electrical power.

Since E = VIt,

Using Ohm's law,

and,

📚 SI Unit

The SI unit of electrical power is watt (W).

Also,

📚 Kilowatt-hour and Unit of Electricity

If a device of power 1 kW operates for 1 hour, the energy used is 1 kWh.

Commercially, 1 unit of electricity = 1 kWh. In some older texts, this is also called a B.O.T. unit.

📚 What Does the Rating of an Electrical Appliance Mean?

If a bulb is marked 220 V, 100 W, it means that the bulb is designed to use electrical energy at the rate of 100 W when connected across the rated potential difference of 220 V.

Its resistance is —

and the current is —

For a 220 V, 100 W bulb —

📚 Example of Electricity Consumption

A house has 2 lamps of 60 W each and 2 fans of 80 W each. All of them operate for 5 hours every day.

Energy used per day —

In 30 days —

Thus, the consumption is 42 units. If the cost per unit is ₹4, the total cost is —

Answer: ₹168

👉 Applications of the Heating Effect

📚 Electric Heater

An electric heater contains a circular support made of heat-resistant and electrically insulating material. Grooves are formed in the support, and a coiled nichrome wire is placed in these grooves. Nichrome is mainly a nickel-chromium based alloy. Its resistivity is much higher than that of copper. Therefore, when electric current passes through the wire, a large amount of heat is produced and the heater becomes hot enough to warm other objects.

If the nichrome wire of the heater is made shorter, its resistance decreases because resistance is proportional to length. If the potential difference remains the same, the current increases. Since H ∝ I², the heat produced also increases.

📚 Electric Iron

The construction of an electric iron is similar to that of a heater. The heated nichrome element warms the smooth metal soleplate at the bottom.

Why is nichrome wire used in electrical heating appliances?

Nichrome has much higher resistivity than copper, so a heating element of suitable resistance can be made using a practical length and thickness of wire. It also resists oxidation at high temperature and does not melt easily. For these reasons, nichrome is widely used in electrical heating appliances.

📚 Why Does the Wire of an Electric Heater Not Glow Like the Filament of an Electric Bulb?

The tungsten filament of an electric bulb is designed so that its temperature becomes extremely high when current passes through it, causing it to become white-hot and emit visible light. In contrast, the length, thickness and resistance of the nichrome heating element in a heater are chosen so that it produces a large amount of heat at a safe operating temperature, but normally does not become white-hot like a bulb filament. Therefore, the primary purpose of a heater is to produce heat, not light.

📚 Fuse Wire

A short wire is connected in series with the mains circuit, usually inside a suitable fuse holder. This is called a fuse wire. During a short circuit, or when too many high-power appliances are used, the current in the line may rise sharply. Excessive current can heat the wiring strongly and may damage insulation or even cause fire. A fuse is therefore connected in the circuit for protection.

A conventional fuse wire is made from a suitable metal or alloy with a relatively low melting point. If the current exceeds a specified safe value, the heat produced in the fuse wire causes it to melt and break the circuit. As a result, current flow stops.

A fuse rated at 10 ampere is designed to disconnect the circuit when the current rises beyond its safe rated limit around that value.

The heating effect of electric current is also used in metal melting, electric furnaces, greenhouse heating and many other applications.

What is meant by a short circuit?

If, for any reason, two conductors at different electric potentials come into direct contact through a path of very low resistance, the total resistance of the circuit becomes very small. As a result, a very large current flows suddenly and a large amount of heat may be produced. This condition is called a short circuit.

👉 Solved Examples

✏️ Example 1

A current of 0.5 A flows through a 10 Ω resistance for 60 s. Find the heat produced.

✏️ Example 2

If the current is increased to 4 times while resistance and time remain unchanged, how many times will the heat produced increase?

Therefore,

Answer: 16 times

✏️ Example 3

A lamp of resistance 440 Ω glows on a 220 V supply for 10 hours. Find the energy consumed in units.

Answer: 1.1 units

Two More Examples of Electricity Consumption

✏️ Example 4

A house has 6 bulbs of 60 W each and 3 fans of 40 W each. All of them run for 6 hours per day for 30 days.

Total power —

Total time —

Energy used —

Thus, the consumption is 86.4 units.

✏️ Example 5

An electrical appliance of 1600 W is connected to a 200 V supply.

Current —

Energy used in 100 hours —

Thus, the consumption is 160 units.

🧠 Quick Revision

⭐ Heat produced = H, electric current = I, time = t, potential difference = V, resistance = R, electrical energy = E, electrical power = P, and mechanical equivalent of heat = J.

⭐ In calories:

⭐ In joules: H = I²Rt = VIt

⭐

⭐ P = VI

⭐ P = I²R

⭐

⭐ E = Pt

⭐ 1 unit = 1 kWh

⭐

✍ Try It Yourself

🔹 A current of 2 A flows through a 5 Ω resistor for 10 minutes. Find the heat produced in joules.

🔹 Find the current and resistance of a 220 V, 60 W bulb.

🔹 How many units of energy will a 1.5 kW heater consume in 2 hours?

🔹 If the current through the same resistance becomes three times, how many times will the heat produced increase in the same time?

🔹 A 500 W appliance runs for 4 hours per day for 30 days. Find the total energy consumed in kWh.