1. The Idea Behind Ohm’s Law
Ohm’s law is a simple relation that connects the three main quantities in an electric circuit: current, voltage and resistance. It tells us how much current will flow through a conductor when a certain potential difference is applied across it.
In everyday terms, voltage pushes the charges, resistance opposes their motion, and current is the result of how fast the charges move.
1.1. Why Ohm’s Law Is Needed
Different materials allow current to flow differently. Some offer very little resistance, while others oppose the flow strongly. Ohm’s law helps quantify this behaviour by giving a direct link between V, I and R.
2. Statement of Ohm’s Law
Ohm’s law states that the current flowing through a conductor is directly proportional to the potential difference across its ends, provided the temperature and other physical conditions remain constant.
2.1. Mathematical Form
\( V \propto I \)
\( V = IR \)
Here:
- V is the potential difference
- I is the current
- R is the resistance of the conductor
This relation works only when the conductor behaves linearly, meaning the V–I graph is a straight line.
2.1.1. Meaning of Resistance
Resistance measures how much the conductor opposes the flow of current. A higher resistance means less current flows for the same voltage. It is given by:
\( R = \dfrac{V}{I} \)
3. Graphical Understanding
The relationship \( V = IR \) can be visualised through a V–I graph. For materials that obey Ohm’s law (called ohmic materials), this graph is a straight line passing through the origin.
3.1. V–I Graph
When voltage is increased in equal steps, the current also increases in equal steps, resulting in a straight-line graph. The slope of this graph gives the resistance.
\( R = \dfrac{V}{I} = \text{slope of V–I curve} \)
4. Understanding Current, Voltage and Resistance Together
Ohm’s law helps relate all three quantities in an intuitive way:
- For a fixed resistance, increasing voltage increases current.
- For a fixed voltage, increasing resistance decreases current.
- For a fixed current, increasing resistance increases the required voltage.
4.1. Small Example
If a conductor has a resistance of \(5\,\Omega\) and a potential difference of \(10\,\text{V}\) is applied across it, the current is:
\( I = \dfrac{10}{5} = 2\,\text{A} \)
5. Limitations of Ohm’s Law
Ohm’s law does not apply to all materials. Some conductors do not maintain a constant resistance when voltage changes. Their V–I graphs are not straight lines.
5.1. Examples of Non-Ohmic Behaviour
- Filament lamps (resistance increases with temperature)
- Semiconductor devices like diodes and transistors
- Electrolytes
For such materials, the relation between V and I is not linear.