Resistance and Ohm's Law

When a voltage is applied across a material, an electrical current flows through it. However, the material itself opposes this current flow. This opposition is called Resistance. Understanding resistance and its relationship with voltage and current is the foundation of all circuit analysis.

What is Resistance?

Resistance ($R$) is a measure of how much a material restricts the flow of electrical current. It is analogous to friction in a water pipe that restricts the flow of water.

The unit of resistance is the Ohm ($\Omega$).

Resistivity and Physical Geometry

The resistance of a specific component (like a wire) depends on both the material it is made of and its physical dimensions.

Resistivity ($\rho$) is a fundamental property of a material. Conductors like copper have a very low resistivity, whereas insulators like rubber have a very high resistivity.

Engineering Meaning: If you double the length of a wire, you double its resistance. If you double its cross-sectional area (make it thicker), you halve its resistance.

Ohm's Law

The fundamental relationship between voltage, current, and resistance was discovered by Georg Ohm. Ohm's Law states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperature remain constant.

The mathematical equation is:

Using Ohm's Law

Ohm's Law can be rearranged depending on the variable you need to find:

• To find voltage: $V = I \cdot R$
• To find current: $I = \frac{V}{R}$
• To find resistance: $R = \frac{V}{I}$

Common Mistakes

1. Assuming Ohm's law applies to everything: Ohm's law strictly applies only to "Ohmic" materials where resistance remains constant regardless of the applied voltage. Non-Ohmic devices like diodes or light bulbs (whose resistance changes with temperature) do not exhibit a linear $V-I$ relationship.
2. Ignoring unit conversions in the resistivity equation: The cross-sectional area of a wire is often given in mm² or AWG. These must be converted to m² before being used in the $R = \rho L/A$ equation.