Find the expression for the resistors connected in series and state its two characteristics. (Draw figure).

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Solution

In various electrical appliances, resistors are often used in combinations. Usually, they are connected either in series or in parallel.
$V = V_{1} + V_{2} + V_{3}$ eq. 1
According to Ohm's law,
$V_{r} = I R_{s}$
(where $R s$ is the effective resistance in series combination)
$V_{1} = I R_{1}$
$V_{2} = I R_{2}$
$V_{3} = I R_{3}$
Substituting these values in equations 1,
$I R s = I R_{1} + I R_{2} + I R_{3}$
$I R s = I (R_{1} + R_{2} + R_{3})$
Striking off ' $I$ ' from the both sides of the equation,
$R_{s} = R_{1} + R_{2} + R_{3}$
Thus, the effective resistance of a series combination of resistance is the sum of individual resistances of the resistors in the combination.
Characteristics of the series combination of resistors are:
(a) The value of the current $^{'} I^{'}$ flowing through the resistors connected in series is the same through each resistor.
(b). The potential difference $^{'} V^{'}$ across the resistors connected in series is equal to the sum of individual potential differences across each resistor.

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