# What is the difference between a series and parallel connection of resistors?

## Answer #1

This is how series and parallel circuit with three resistances \(R_1\), \(R_2\) and \(R_3\) looks like:

You can see the first difference in the circuits and namely how the resistors are connected together:

In a series circuit, the positive pole of the voltage source that supplies the voltage \(U\) is connected to

*a single resistor*\(R_1\) and the negative pole is also connected to a single resistor, namely \(R_3\). The resistors in a series circuit form a chain to which you apply a voltage \(U\).In a parallel circuit, on the other hand, you connect the positive pole of the voltage source

*to three*ends of the three resistors, and you do the same with the negative pole.

Furthermore, a parallel circuit differs from a series circuit of resistors in the following points:

In a series circuit, the

*same*current \(I\) flows through all three resistors:**Formula: Total current is equal to the individual currents in a series circuit**Formula anchor $$ \begin{align} I ~=~ I_1 ~=~ I_2 ~=~ I_3 \end{align} $$In a parallel circuit, on the other hand,

*different*currents \(I_1\), \(I_2\), and \(I_3\) flow through the resistors. The total current is the sum of the individual currents:**Formula: Total current is equal to the sum of the individual currents in a parallel circuit**Formula anchor $$ \begin{align} I ~=~ I_1 ~+~ I_2 ~+~ I_3 \end{align} $$In a series circuit, a

*different*voltage \(U_1\), \(U_2\) and \(U_3\) is applied to each resistor. The total voltage \(U\) is the sum of the individual voltages:**Formula: Total voltage is the sum of the individual voltages**Formula anchor $$ \begin{align} U ~=~ U_1 ~+~ U_2 ~+~ U_3 \end{align} $$In a parallel circuit, on the other hand, the

*same*voltage \(U\) is applied to all three resistors:**Formula: Total voltage is equal to the individual voltages**Formula anchor $$ \begin{align} U ~=~ U_1 ~=~ U_2 ~=~ U_3 \end{align} $$The total resistance \(R\) of a series circuit is obtained by

*adding all individual resistances*:**Formula: Total resistance is equal to the sum of the individual resistances**Formula anchor $$ \begin{align} R ~=~ R_1 ~+~ R_2 ~+~ R_3 \end{align} $$In a parallel circuit, however, the total resistance is

*not the sum of the individual resistances*:**Formula: The reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances.**Formula anchor $$ \begin{align} \frac{1}{R} ~=~ \frac{1}{R_1} ~+~ \frac{1}{R_2} ~+~ \frac{1}{R_3} \end{align} $$