In this section, we will discuss on the Joule's Law of Heating.
In 1841, Joule studied the heating effect of an electric current. He found that, the amount of heat $H$ is produced when an electric current is passed through a conductor after a certain time, called Joule's Heating Effect.
$H = I^2\,R\,t$ .......... (i)
Where, $H$ = amount of heat; $I$ = flow current through a conductor; $R$ = Resistance; $t$ = time taken.
Many electrical devices such as electric heater, soldering iron, electric iron, electric bulb etc. are the example of Joule's heating effect.
Iron used to remove wrinkles from Clothes
Soldering iron, used to melt solder
Mathematically;
1) The amount of heat produced in current conducting wire, is proportional to square of the current flow through the circuit, at constant electrical resistance and time of current flow.
i.e. $H ∝ I^2$ .......... (ii)
2) The amount of heat produced is proportional to the electrical resistance of the wire, at constant current and time of current flow.
i.e. $H ∝ R$ .......... (iii)
3) The amount of generated heat due to a flow of current is proportional to the time of current flow, at constant electrical resistance and amount of current flow.
i.e $H ∝ t$ .......... (iv)
When all these 3 - situation are put together, the resulting formula is,
$H ∝ I^2\,R\,t$
or, $H = \frac{ I^2\,R\,t}{J}$ .......... (v)
Where, $J = 4.18\, J\,cal^{-1}$ is called Joule's Mechanical Equivalent of Heat. It is a conversion factor only.
Expression of Heat developed in a wire:
Let $I$ be the current passing through the resistance, at time $t$. The total charge passing through $A$ to $B$ is,
$Q = I\,t$ (∵$ I = \frac{Q}{t}$) .......... (i)
Potential difference ($V$) between $A$ to $B$ is,
$V = I\,R$ .......... (ii)
Work done to transfer the charge $Q$ from point $A$ to $B$ is,
$W = Q\,V$ .......... (iii)
From equation (i), (ii) and (iii), we get
$W = I\,t. I\,R$
or, $W = H = I^2\,R\,t$ .......... (iv)
This equation (iv) is the expression for heat developed.
Its ability to oppose the flow of charge through it. In general, the resistance is the ratio of the potential difference across an electrical component to the current passing it.
Mathematically,
$R = \frac{V}{I}$ .......... (i)
Where, V = Voltage and I = Current. It's unit is ohm $(\Omega)$ in SI unit.
The one ohm $(1 \; \Omega)$ of the conductor is defined as, if one ampere current flows through the resistance under a potential difference of one volt. i.e.
$1\; \Omega = \frac{1\; Volt}{1\; Ampere}$ .......... (ii)
Click here for the Resistance Colors code
» Resistivity(Symbol $\rho$):
The electrical resistivity of a conductor (material) is a measure of how strongly the material opposes the flow of electric current through it. The resistivity is depends upon the lengths and cross-sectional areas of the conductor. The higher the resistivity $\rho$ the more the resistance and vice-versa.
For example: The resistivity of a copper (good conductor) is in the order of 1.72 * 10$^-8$ Ω m. Whereas the resistivity of a air (insulator / poor conductor) 10$^{10}$ 10 $^{14}$ Ω m.
The resistivity of a conductor s defined as the resistance of the conductor of unit cross-sectional area per unit length. It's unit is ohm meter (Ω m), in SI system.
$\rho = R\frac{A}{l}$ .......... (iii)
Mathematically,
Let length $l$ of the conductor having resistance $R$ and its cross sectional area $A$.
At constant temperature,
The resistance $R$ of the conductor is directly proportional to the length $l$ of the conductor.
$R ∝ l$ .......... (iv)
And, the resistance $R$ of the conductor is inversely proportional to the cross sectional area $A$.
$R ∝ \frac{1}{A}$ .......... (v)
From equation (iv) and (v), we get
$R ∝ \frac{l}{A}$
or, $R = \rho \frac{l}{A}$ .......... (vi)
Where $\rho$ is a proportionality constant called 'Resistivity of a conductor'.
Ohm's Law (V = IR): is a fundamental formula in an electronics. It is used to calculate the relationship between voltage (V), current (I) and resistance (R) in an electrical circuit.
Ohm's Law states that: "The Current through a conductor between two points is directly proportional to the voltage (Potential difference) across the two points" i.e.
$V ∝ I$
$V = I\,R$ .......... (i)
Where $R$ is a proportionality constant called resistance (R) of the conductor. This equation (i) is the mathematical form of Ohm's Law.
An electric circuit is formed when a conductive path is created to allow free electrons to move continuously. This continuous movement of free electrons through the conductor of a circuit is called a Current (I).
The force motivating electrons to flow in a circuit is called Voltage (V). The voltage is a specific measure of potential energy that is always relative between two points.
Free electrons tends to move through conductors with some degree of friction (or, opposition to motion), called Resistance (R).
The amount of current in a circuit depends on the amount of voltage available to motivate the electrons, and the amount of resistance in the circuit to oppose electron flow (Ohm's Law).
Let $I$ be the current passing through the resistance, at time $t$. The total charge passing through $A$ to $B$ is,
