Ohm's Law

Ohm's Law

Is there a relationship between the potential difference across a conductor and the current through it? If we connect a nichrome wire to a varying number of cells and measure $V$ and $I$ each time, we find that the ratio $V/I$ stays constant. A graph of $V$ against $I$ is a straight line through the origin.

In 1827, Georg Simon Ohm stated this as Ohm's law:

The potential difference $V$ across the ends of a given metallic conductor is directly proportional to the current $I$ through it, provided its temperature remains constant.

$$V \propto I \quad \Rightarrow \quad V = IR$$

Resistance and the Ohm

The constant $R$ is the resistance of the conductor - its property of opposing the flow of charge:

$$R = \frac{V}{I}$$

The SI unit of resistance is the ohm (Ω). If a potential difference of 1 V drives a current of 1 A, the resistance is 1 ohm:

$$1\ \Omega = \frac{1\ \text{volt}}{1\ \text{ampere}}$$

Rearranging gives $I = V/R$. So for a fixed voltage, the current is inversely proportional to the resistance - double the resistance, and the current halves.

A rheostat (variable resistance) is a component used to change the current in a circuit without changing the voltage source.

[Exam Tip] Slope of the $V$–$I$ graph = resistance $R$. A steeper line means a larger resistance. Ohm's law holds only at constant temperature.

Solved Examples

Example 1: Current drawn by a bulb and a heater (NCERT 11.3)

(a) How much current will a bulb of filament resistance 1200 Ω draw from a 220 V source? (b) How much current will a heater coil of resistance 100 Ω draw from the same source?

Solution: (a) $I = V/R = 220/1200 = 0.18\ \text{A}$. (b) $I = V/R = 220/100 = 2.2\ \text{A}$. The heater draws much more current than the bulb from the same 220 V source.

Example 2: Heater current at higher voltage (NCERT 11.4)

The potential difference across a heater is 60 V when it draws 4 A. What current will it draw at 120 V?

Solution: $R = V/I = 60/4 = 15\ \Omega$ (constant). At 120 V: $I = V/R = 120/15 = 8\ \text{A}$.

Example 3: Effect of halving the voltage

The resistance of a component is constant. If the potential difference across it is halved, what happens to the current?

Solution: From $I = V/R$ with $R$ constant, $I \propto V$. Halving $V$ halves the current.

Example 4: Resistance from a V–I reading

A resistor carries 2 A when 10 V is applied. Find its resistance.

Solution: $$R = \frac{V}{I} = \frac{10\ \text{V}}{2\ \text{A}} = 5\ \Omega$$