**Ohm’s Law** is an empiric relation, accurately describing the conductivity of a material. It defines the relationship between the electric current passing through a circuit and the potential difference between two points of the circuit.

Index

**History**

Ohm’s law was named after the German physicist* Georg Simon Ohm* published a treatise in 1827, that described the measurements of applied voltage and current through simple electric circuits.

**Ohm’s Law Explained**

**Statement**

The law states that current passing through a conductor between two points is directly proportional to the voltage across the two points.

**Mathematical Equation**

\(I \propto V\)

\(I = \frac{V}{R}\)

Where,

\(I\) – Current passing through the circuit/conductor (amperes, A)

\(V\) – Voltage difference between two points (volts, V)

\(R\) – Resistance of the conductor material(ohms, Ω)

The law can also be used to say that the resistance of a wire remains constant, independent of the current. Although the law describes conductivity of various electrically conductive materials, some materials do not obey the law. Such materials are called **non-ohmic materials**.

The law also depends on the temperature and other physical factors to be constant.

The Ohm’s law is also generalised in **electromagnetics** in the form:

\(J = \sigma E\)

Where,

\(J\) – Current Density at a location of a material

\(\sigma\) – Conductivity

\(E\) – Electric field at that location

**Limitations of Ohm’s Law**

Ohm’s law, unfortunately, cannot be applied to unilateral networks. This is because, in unilateral networks current flows in only one direction.

The law is also not applicable to non-linear elements due to changes in resistance, when the voltage or current is changed.

**Applications of Ohm’s Law**

- This law can be used to determine the voltage, resistance or current of an electric circuit, provided the other two values are known.
- It is used in DC ammeters.
- The power dissipated from various electric appliances can be determined using Ohm’s law.

**Examples**

**Question 1.** Resistance of an electric appliance is 20 Ω. Current passing through the appliance is 4A. Find the voltage between any two points.

**Solution.** As, \(V= IR\)

⇒ \(V = \frac{I}{R}\)

⇒ \(V = 20*4\)

∴ \(V = 80V\)

** Question 2.** What will be the new resistance of a wire, if it is stretched 4 times its original length?

**Solution.** Let the original resistance by \(R\) and the new resistance be \(R_{\mbox{new}}\). Let original length of wire be \(l_1\), area of cross section of wire be \(A_1\). Let the new length be \(l_2\) and area of cross section be \(A_2\).

As,

\(R = \rho \frac{l_1}{A_1} … (1)\)

⇒ \(R_{\mbox{new}} = \rho \frac{l_2}{A_2} = \rho \frac{8l_1}{A_2} … (2)\)

Even though the wire is stretched, its volume remains the same.

⇒ \(A_1 l_1 = A_2 l_2\)

⇒ \(\frac{A_1}{A_2} = 4 … (3)\)

Dividing (1) by (2),

\(\frac{R_{\mbox{new}}}{R} = \frac{\rho (8l_1)}{A_2}*\frac{A_1}{\rho l_1}\)

⇒ \(\frac{R_{\mbox{new}}}{R} = \frac{A_1}{A_2}*4\)

Substituting (3) above,

⇒ \(\frac{R_{\mbox{new}}}{R} = 4*4 = 16\)

⇒ \(R_{\mbox{new}} = 16*R\)

Hence the new resistance is 4 times greater than the original resistance of the wire.

**FAQs**

**What is Ohm’s law?**Ohm’s law is a relationship between the current passing through a conductor and the voltage difference between any two points on the conductor.

**Why is Ohm’s law not applicable for semiconductors?**Semiconductors are nonlinear materials i.e., the resistance of such materials change on changes in voltage or current. This is why Ohm’s law is not applicable for semiconductors.