Resistances in Series and Resistances in Parallel
More than one electrical resistance can be connected either in series or in parallel in addition to that, more than two resistances can also be connected in combination of series and parallel both. Here we will discuss mainly about series and parallel combination.
Resistances in SeriesSuppose you have, three resistors, R1, R2 and R3 and you connect them end to end as shown in the figure below, then it would be referred as resistances in series. In case of series connection, the equivalent resistance of the combination, is sum of these three electrical resistances.
That means, resistance between point A and D in the figure below, is equal to the sum of three individual resistances. The current enters in to the point A of the combination, will also leave from point D as there is no other parallel path provided in the circuit. Now say this current is I. So this current I will pass through the resistance R1, R2 and R3. Applying Ohm’s law, it can be found that voltage drops across the resistances will be V1 = IR1, V2 = IR2 and V3 = IR3. Now, if total voltage applied across the combination of resistances in series, is V.
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Then obviously Since, sum of voltage drops across the individual resistance is nothing but the equal to applied voltage across the combination.
Now, if we consider the total combination of resistances as a single resistor of electric resistance value R, then according to Ohm’s law, V = IR ………….(2)
Now, comparing equation (1) and (2), we get So, the above proof shows that equivalent resistance of a combination of resistances in series is equal to the sum of individual resistance. If there were n number of resistances instead of three resistances, the equivalent resistance will be