Question

When do you say that the resistors are connected in series? Find the expression for the resistors connected in this way. (Draw circuit diagram).

Answer 1

Resistors in Series : If the number of resistance are connected one after another in such a way that the same current flows through each resistance, then the arrangement is called resistance in series. $I$ is the current, $V$ is the PD across $C$ and $D$, the three resistors $R_1$, $R_2$ and $R_3$ are connected in series between points $C$ and $D$. $R_s$ is the effective resistance in the circuit and $V_1$, $V_2$ and $V_3$ are the potentials across the three resistors.
$V=V_1+V_2+V_3$ ........(1)
By Ohm's Law,
$V=I{R}_s$
$V_1=I{R}_1$, $V_2=I{R}_2$, $V_3=I{R}_3$
Substituting these values in equation no. 1
$I{R}_s=I{R}_1+I{R}_2+I{R}_3$
$I\left(R_s\right)=I(R_1+R_2+R_3)$
$\therefore$ $R_s=R_1+R_2+R_3$
For '$n$' number of resistors connected in series
$R_s=R_1+R_2+R_3+$..........$R_n$.
Characteristics of series combination of resistors :
(1) In series combination current through each resistor is constant.
(2) In series combination potential difference across each resistance is different depending upon the value of resistance.