Find the expression for the resistors connected in series. Write any two characteristics of series combination of resistors.

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Solution

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
$I R_{s} = I R_{1} + I R_{2} + I R_{3}$
$I (R_{s}) = I (R_{1} + R_{2} + R_{3})$
$∴$ $R_{s} = R_{1} + R_{2} + R_{3}$
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.

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