Series and Parallel Circuits

In a series circuit, circuit components are connected in a single loop, one after another. 

The same flow of charge passes through each circuit component and so the current is the same in every component:

\textcolor{aa57ff}{\text{I}_{\text{total}}=\text{I}_1=\text{I}_2=\text{I}_3=\text{...}}

The battery or cell provides the supply of potential difference to the circuit.  The potential difference is shared between the other components. So the total potential difference is equal to the potential difference of the battery:

\textcolor{aa57ff}{\text{V}_{\text{s}}=\text{V}_1+\text{V}_2+\text{V}_3+\text{...}}

Resistances in series adds up:

\textcolor{aa57ff}{\text{R}_{\text{total}}=\text{R}_1+\text{R}_2+\text{R}_3+\text{...}}

In parallel circuits, components are connected in separate loops. 

Each charge can only flow through one of the loops and so current is shared between loops. So the supply current in the loop with battery is equal to the sum of the current in the other loops:

\textcolor{f21cc2}{\text{I}_s=\text{I}_1+\text{I}_2+\text{I}_3+\text{...}}

The potential difference is the same in every loop: 

\textcolor{f21cc2}{\text{V}_1=\text{V}_2=\text{V}_3}

When resistors are connected in parallel, the supply current is shared between the resistors and so the overall resistance is reduced as the electrical charges may take many paths.