Combination of Resistors – Series

The current through a single resistor R across which there is a potential difference V is given by Ohm’s law I = V/R. Resistors are sometimes joined together and there are simple rules for calculation of equivalent resistance of such combination.

 Two resistors are said to be in series if only one of their end points is joined.

Consider two resistors R₁ and R₂ in series. The charge which leaves R₁ must be entering R₂. Since current measures the rate of flow of charge, this means that the same current I flows through R₁ and R². By Ohm’s law:

Potential difference across R₁ = V₁ = I R₁, and Potential difference across R₂ = V₂ = I R₂.

The potential difference V across the combination is V₁+V₂. Hence, V = V₁+ V₂ = I (R₁ + R₂).

This is as if the combination had an equivalent resistance R_eq, which by Ohm’s law is