More than one resistances in series and parallel can be connected, in addition to that more than two resistances in series and parallel can also be connected in combination. Resistors can be connected together in an unlimited number of series and parallel combinations to form complex resistive circuits.

But what if we want to connect various resistors together in “BOTH” parallel and series combinations inside a similar circuit to deliver progressively complex resistive systems, how would we ascertain the joined or all out circuit resistance, currents and voltages for these resistive combinations.

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# Resistances in Series and Parallel Combinations

Resistor circuits that combine series and parallel resistors networks together are generally known as **Resistor Combination** or mixed resistor circuits.

The method of calculating the circuits equivalent resistance is equivalent to that for any individual series or parallel circuit and ideally we presently realize that resistors in series convey the very same current and that resistors in parallel have the very same voltage crosswise over them. Here we will discuss mainly about series and parallel combination.

## Resistances in Series

Suppose you have, three resistors, R_{1}, R_{2} and R_{3} and you connect them end to end as shown in the figure beneath, at that point it would be alluded as **resistances in series**.

In case of series connection, the equivalent resistance of the combination, is aggregate of these three electrical resistances. That implies, resistance between point An and D in the figure underneath, is equivalent to the aggregate of three individual resistances.

The current enters in to the point A of the combination, will likewise leave from point D as there is no other parallel way given in the circuit.

Now say this current is I. So this current I will go through the resistance R_{1}, R_{2} and R_{3}. Applying Ohm’s law, it very well may be discovered that voltage drops over the resistances will V_{1} = IR_{1}, V_{2} = IR_{2} and V_{3} = IR_{3}. Presently, if all out voltage connected over the combination of **resistances in series**, is V. 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)

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Now, comparing equation (1) and (2), we get

So, the above proof shows that equivalent resistance of a combination of resistances in series is equivalent to the aggregate of individual resistance. If there were n number of resistances rather than three resistances, the proportional resistance will be

## Resistances in Parallel

Let’s three resistors of resistance value R_{1}, R_{2} and R_{3} are connected in such a way, that correct side terminal of every resistor are associated together as appeared in the figure beneath, and furthermore left side terminal of every resistor are additionally associated together.

This combination is called **resistances in parallel**. If electric potential difference is connected over this combination, that point it will draw a current I (say).

As this current will get three parallel paths through these three electrical resistances, the current will be divided into three parts. Say currents I_{1}, I_{1} and I_{1} pass through resistor R_{1}, R_{2} and R_{3} respectively.

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Where total source current

Now, as from the figure it is clear that, each of the **resistances in parallel**, is over a similar voltage source, the voltage drops over every resistor is same, and it is same as supply voltage V (say). Consequently, as per Ohm’s law,

Now, if we consider the equivalent resistance of the combination is R. Then,

Now putting the values of I, I_{1}, I_{2} and I_{3} in equation (1) we get,

The above expression represents equivalent resistance of resistor in parallel. If there were n number of resistances connected in parallel, instead of three resistances, the expression of equivalent resistance would be

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### Resistances in Series and Parallel Combinations Conclusion

After going through the above portion of resistances in series and parallel we can now establish a resistances in series and parallel combinations. I hope you enjoy when reading this article, thank you.