Draw circuit diagram of three resistances connected in series combination. Derive formula for equivalent resistance for this combination.

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Solution

The diagram of three resistors connected in series combination is shown.

$R_{1}, R_{2}$ and $R_{3}$ are the three resistors.
$I$ = electric current flowing through the circuit
$V$ = the potential difference supplied by the battery
Applying the Ohm’s law to the entire circuit, we have
$V = I R$
On applying Ohm’s law to the three resistors separately, we further have
$V_{1} = I R_{1}$
$V_{2} = I R_{2}$
and $V_{3} = I R_{3}$
The total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistors. That is,
$V = V_{1} + V_{2} + V_{3}$
Therefore, $I R = I R_{1} + I R_{2} + I R_{3}$
or
Equivalent resistance of the combination, $R = R_{1} + R_{2} + R_{3}$

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