*Before going through these derivations it is advertised that you read up on Kirchhoff’s two laws and read through resistors in series and parallel first.*

Using the following circuit setup and Kirchhoff’s laws, the equation for resistors in series can be derived;

Kirchhoff’s voltage law (KCL) tells us that (1)

Since Â we can write;

*The power source is providing power to the entire circuit which consists of ALL the resistors, *

So we can now sub these into equation (1) and write;

(2)

Kirchhoff’s current law (KCL) tells us that because this is a series circuit the current is the same through both resistors and so;

Therefore equation (2) becomes;

Divide the whole equation by to give:

Expanding this equation for more than just two resistors in series and we can write the full equation;

Further reading:

- Isaac Physics – Kirchhoff’s Laws – This is a reading resource