Resistances in Series

When a number of resistances are connected in head to tail manner one after another in series is called resistances connected in series or simply resistances in series. We sometimes also call it series resistances.  

The equivalent resistance of a series combination of resistances is algebraic sum of all the resistances connected in series.  

Resistances in Series
Resistances in Series

The voltage drop across the series resistances is also the algebraic sum of the voltage drops across individual resistance.  

Let us connect three resistances of value R1, R2 and R3 in series as shown below.

Series Connected Resistances
Series Connected Resistances

Let us connect one battery of voltage V volt across the series combination of the resistances.  

We will also consider that the voltage drop across R1 is V1, the voltage drop across R2 is V2, and the voltage drop across R3 is V3.

As all three resistances are connected in series the same current will flow through the common path. Let us assume the current is I. 

Hence, voltage drop across the resistance R1 is IR1.

Voltage drop across the resistance R2 is IR2.

Voltage drop across the resistance R3 is IR3.

So we can write  

From that we can ultimately write that  

This is the equivalent resistance of the series combination of three resistances. It instead of three resistances there were n number of resistances connected in series, then the equivalent resistance of the series combination would be written as  

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