Heating Effect of Electric Current

The heating effect of electric current is the phenomenon in which electrical energy is converted into heat energy when current flows through a conductor. This happens because moving electrons collide with the atoms of the conductor, producing heat. When current passes through a high-resistance wire (like nichrome), the wire becomes hot and generates heat.

In electrical circuits, part of the electrical energy supplied by the source is used for useful work, while the remaining energy is dissipated as heat due to resistance. This conversion of electrical energy into heat is called the heating effect of current.

Effects of Heat on the Conductor

• Electrical energy is partially transformed into heat energy when charges move through a conductor.
• The amount of heat produced depends on the current, resistance of the conductor, and time of flow.
• This heat can be harnessed in devices like heaters, toasters, and electric irons for practical purposes.

Do You Know

• In metals (conductors) : Resistance increases with temperature.
• In semiconductors : Resistance decreases with temperature.

Joules Law of Heating

Physicist James Prescott Joule stated that the heat produced in a conductor due to electric current is directly proportional to the square of the current, the resistance of the conductor, and the time for which the current flows. The heat generated is measured in joules.

\boxed {H = I^2 . \, R . \, t}

where,

• H = Heat Produced (J).
• I = Current (A)
• R = Resistance (Ω)
• t =Time (s)

Heating Effect Formula Derivation

Assume a current I flows through a resistor of resistance R and the potential difference across the circuit is V. If a charge Q flows in time t the work done in moving this charge through potential difference V is equal to the electrical energy supplied.

Current is defined as: I = \frac{Q}{t}

Electrical power: P = V \times I

Energy supplied in time t: E = P \times t = VI.t

Since electrical energy converts into heat: H = VIt

Using Ohm’s Law (V=IR) ⇒ H = I^2 R t

The Heat produced in a conductor depends on :

According to Joule’s Law of Heating: H = I^2 . \, R . \, t

1. Directly Proportional to the Square of Current (for constant resistance and time) H ∝ I²

This means:

• If the current is doubled, the heat produced becomes four times.
• If the current is halved, the heat produced becomes one-fourth.

Hence, a small increase in current produces a large increase in heat.
Greater the current, greater is the heat produced.

2. Directly Proportional to Resistance (for constant current and time) H ∝ R

This means:

• A wire with higher resistance (such as nichrome) produces more heat.
• A wire with lower resistance (such as copper) produces less heat.

Therefore, materials with high resistance are used in heating appliances.

3. Directly Proportional to Time (for constant current and resistance) H ∝ t

This means:

• If an electrical device is used for a longer duration, it produces more heat.
• If it is used for a shorter duration, it produces less heat.

Thus, the longer the current flows through a conductor, the greater the heat generated.

Related Articles

• Electric Current
• Heat and Temperature
• Chemical Effects of Electric Current

Solved Examples

Example 1: 100 J of heat energy is produced by an electrical appliance that is used for 1 sec and is having a resistance of 4 ohms. Find and calculate the potential difference of the appliance.

Solution: As we know,

H = I²×R×t

Given, H = 100 J, R = 4 ohm, t = 1 sec

Therefore, 100J=I²×4×1

\therefore I^{2} = \frac{100}{4} =25

\therefore I =5 A

From ohm’s law we know

V=I×R

Therefore, V = 5A × 4Ω

V = 20 V

Therefore, the potential difference generated is 20 V.

Example 2: Find out the heat produced by the electric toaster when it is used for 5 minutes. The current given was 2 A and its resistance is 3 ohms.

Solution: As we know,

H = I²×R×t

Given, I = 2 A, R = 3 ohm, t = 5 min = 300 sec

Therefore, H=2²×3×300J

H = 22×900 J

Therefore, H=4×900 J

H = 3600 J

Hence, the heat that is produced or liberated by the electrical toaster is 3600 J.

Example 3: The heat generated is 100 J from an electrical fan which has a potential difference of 10 V and the time for which it is used is 10 sec. Find what the amount of electrical current that is used is?

Solution: As we know,

H = V × I × t

Given, H = 100 J, V = 10 V, t = 10 sec

Therefore, 100J=10V×I×10

∴100J = 100 × I

\therefore I = \frac{100}{100} A

I = 1 A.

Therefore, the current used is 1 A.

Example 4: What is the power consumed if a device or appliance is operated at 1 V potential difference and 6 A current?

Solution: As we know,

P = V × I

Given, V = 1V AND I = 6 A

P = 1 V × 6 A

P = 6 W

Hence, the power that has been consumed is 6 W.

Example 5: What is the power consumed if a toaster having 3-ohm resistance is operated at 1 A current?

Solution: As we know,

P = I² × R

Given, I = 1 A and R = 3 ohm

∴P = 1² × 3Ω

P = 3 W.

Therefore, the power consumed has been calculated to be 3 W.

Unsolved Problems

Question 1: An electric heater works at a potential difference of 220 V and draws a current of 5 A. Find power consumed and heat produced in 2 minutes.

Question 2: A resistor of resistance 10 Ω is connected to a battery and produces 4500 J of heat in 5 minutes.
Calculate the current flowing through the resistor.

Question 3: An electric bulb produces 800 J of heat in 40 seconds when a current of 2 A flows through it.
Find the resistance of the bulb.

Question 4: Two resistors of 4 Ω and 6 Ω are connected in series to a 10 V battery. Calculate total resistance, current in the circuit and heat produced in 5 minutes in the 6 Ω resistor only.

Question 5: An electric iron operates at 220 V and has a resistance of 44 Ω. If it is used for 15 minutes calculate current drawn, power consumed and heat produced.

Question 6: A heater produces 7200 J of heat in 10 minutes when connected to a power supply. If the current flowing is 3 A. Find resistance of the heater potential difference across it.