[Physics Class Notes] on Joule's Law Pdf for Exam

The amount of heat that is produced within an electric wire due to the flow of current is expressed in the unit of Joules. When the current flows through the wire there is a collision between electrons and atoms of the wire which leads to the generation of heat. Joule’s Law states that when a current flows in a conductor the amount of heat generated is proportional to current, resistance, and time in the current flowing. Let us have a look at the concept behind the joule’s law.

Mathematical Representation of Joule’s Law

1. When in a current conducting wire the time of the flowing of current and the resistance of the wire is constant, the amount of heat produced and the square of the amount of current flowing the wire are proportional to each other.

Equation 1 :  [H alpha i^{2}] (Where R and T are Constant)

2. When in a current conducting wire the time of the flowing of current and the current of the wire are constant, the amount of heat produced and the amount of electrical resistance of the wire are proportional to each other.

Equation 2: [H alpha R] (Where R and T are Constant)

3. When in a current conducting wire the amount of the electrical resistance and the amount of current are constant, the heat produced and the time of current flowing are proportional to each other.

Equation 3: [H alpha t] (Where R and i are Constant)

Formula of Heat

When equations 1, 2, and 3 are merged, the resulting formula is-

[H alpha i^{2}. Rt] (i, R, and t are variables)

[H = frac{1}{J}.i^{2}RT]  (where J is a Joule’s Constant)

The joule’s constant J is defined as the number of work units that furnishes one unit of heat when converted completely into heat. 

The value of J= 4.2 joules/cal.

[H = frac{1}{J}.i^{2}RT] 

[H = frac{i^{2}Rt Joules}{frac{4.2 Joules}{cal}}]  

= [ frac{i^{2}Rt}{4.2 Joules}]

= [ frac{i^{2}Rt}{4.2 Joules}]

= [0.24 i^{2} Rt cal]

According to Joule’s law 

[I^{2} Rt] = work done in joules when through a resistor of R ohmsi Ampere of current is maintained for t seconds.

[H = 0.24 Vit cal = 0.24frac{v^{2}}{R}cal (V = iR)]

Electrical Power

The rate at which the work is done in an electric circuit in order to maintain the steady current is known as the electrical power of that circuit. It can also be stated as the rate at which the electrical energy is converted into other forms of energy. The SI unit of electrical power in watts W.

[P = frac{w}{t} = frac{I^{2}Rt}{t}]

[P = I^{2}R = IV = frac{V^{2}}{R}]