Joule’s law Formula
When current is flowing through the wire the heat is produced in wire and this heat is produced due to the collision of electrons in the wire. This law show the relationship between heat produce by electric current flowing through a circuit or conductor. This is joules 1st law.
The law states that the heat developed in conductor is equal to the product of the square of the current, the resistance and time.
Consider a circuit the current ‘i’ passing through the conductor of resistance ‘r’ for time ‘t’.
Mathematically, from statement
H = I2 Rt —– (1)
Where, H = heat produced
I = current in the conductor
R = Resistance
t = time taken
From equation (1) we can say that, heat produced is directly proportional to
(i) Square of current for a given resistance
(ii) Directly proportional to resistance
(iii) Directly proportional to the time taken for current flows through resistor.
I = √H/Rt ——- (2)
Equation (1) is law of heating.
Numericals on Joule’s law Formula:
(1) The current of 5 A is flows through resistor of resistance 7Ω for 3 minute. Calculate the heat energy produced in resistance?
Given
R = 7Ω
I = 5 A, t = 3 minute = 60×3 = 180 sec
H = ?
H = I2Rt
H = (5)2 × 7 × 180
H = 25 × 7 × 180
H = 31,500 J
∴ The heat produced in resistance 7 Ω is 31,500 J.
(2) 3000 J of heat produced in 5sec in 8 Ω resistance. Calculate the potential difference?
Given:
H = 3000 J
R = 8 Ω
t = 5 sec
V =?
I = √H/Rt = √[3000/(8×5)]
= √3000/(40)
I = √75 = 8.66A
From Ohm’s law
V = IR = 8.66 × 8 = 69.28V
V = 69.28 V
∴ The potential difference is 36.28 V.
Important Faq
Q.1) What are common applications of Joule’s law?
Answer: The common applications of Joule’s law are given as follows
- Filament used in bulb works on Joule’s law
- The working of electric fuse is based on Joule’s law
- Electric heater, geyser, microwave oven toaster etc works on Joule’s law.
- Platinum wire/rod used in surgery also based on Joule’s law.
Q.2) Why heat is produced in conductor when current flows through it?
Answer: During flow of current large number of electron flows from one end to another end in conductor in electric field. These electron consistently collide on ions boundaries and on neighbouring atoms so electrons has to do work against the frictional forces which results in dissipating in its kinetic energy. As per the law of conservation of energy this dissipated kinetic energy could be regain by producing heat energy.
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