Explain the series connection of resistors. Derive the equation for the equivalent resistance $(R_S)$.

(N/A) When two or more resistors are connected end-to-end such that the same amount of current flows through each of them,the connection is called a series connection.
In a series connection,the total potential difference $(V)$ across the combination is equal to the sum of the potential differences across each individual resistor.
Consider two resistors $R_1$ and $R_2$ connected in series between points $A$ and $B$ as shown in the figure. $A$ current $I$ flows through both resistors.
According to Ohm's law,the potential difference across resistor $R_1$ is:
$V_1 = I R_1$ ... $(1)$
The potential difference across resistor $R_2$ is:
$V_2 = I R_2$ ... $(2)$
The total potential difference $V$ across the combination is:
$V = V_1 + V_2$
Substituting the values from $(1)$ and $(2)$:
$V = I R_1 + I R_2$
$V = I (R_1 + R_2)$
If $R_S$ is the equivalent resistance of the series combination,then by Ohm's law:
$V = I R_S$
Comparing the two expressions for $V$:
$I R_S = I (R_1 + R_2)$
$R_S = R_1 + R_2$
Thus,for $n$ resistors in series,the equivalent resistance is $R_S = R_1 + R_2 + ... + R_n$.