# Difference between Resistances in Series and Parallel

In electric circuits, resistance (or resistor) is one of the elementary component. The resistors are connected in different fashion in an electric circuit, such as series, parallel and series-parallel, etc. This article is meant for explaining the differences between combination of resistances in series and parallel. Also, we have briefly explained the series combination and parallel combination of resistances.

## Resistances in Series

When two or more resistances are connected end to end, i.e. the ending terminal of one resistance is connected to starting terminal of second resistance, and the ending terminal of second resistance to the starting end of third resistance and so on, and there is only one path for current to flow, then this combination of resistances is known as series combination of resistances.

In case of series combination of resistances, the voltage drop across each resistance is different and depends on the value of the resistance. Therefore, the series combination of resistances is also used as a voltage divider circuit.

If n-resistances are combined in series, then the equivalent resistance of the combination is given by,

$$R_{series}\:=\:R_1\:+\:R_2\:+\:R_3\:+\:\dotsm\:+\:R_n$$

## Resistances in Parallel

When one end of all the resistances is connected to a common point and the other end of all the resistances is connected to another common point, so that there are as many number of paths for current flow as the resistances, then this is known as parallel combination of resistances.

Since the parallel combination of resistances divides the total circuit current in different branches depending upon the value of resistance. Hence, the resistances in parallel are also used as a current divider circuit.

When "n" resistances are joined in parallel, then the equivalent resistance of the combination is given by,

$$\frac{1}{R_{parallel}}\:=\:\frac{1}{R_1}\:+\:\frac{1}{R_2}\:+\:\frac{1}{R_3}\:+\:\dotsm\:+\frac{1}{R_n}$$

## Difference between Resistances in Series and Parallel

Series and parallel are the two methods of combining resistances in electric circuits. However, there are many differences between resistances in series and resistances in parallel that are listed in the following table-

ParameterResistances in SeriesResistances in Parallel
DescriptionWhen the resistances are connected together such that there is only one path for current flow, it is known as series combination of resistances.When the resistances are joined together such that the number of paths for current flow are equal to the number of resistances in the combination, then it is known as parallel combination of resistances.
CurrentThe electric current remains the same in all the resistances in series connection.The current flowing through each resistance in parallel connection is different, it depends upon the value of resistance.
VoltageThe voltage across each resistance in series connection is different, it depends upon the value of resistance.The voltage remains the same across all the resistances in parallel connection.
Number of current pathsThere is only one path for current flow in the series connection of resistances.The number of paths for current is equal to the number of resistances connected in parallel.
Also known asThe series connection of resistances is also known as voltage divider.The parallel connection of resistances is also known as current divider.
Expression of equivalent resistanceFor series connection of resistances, the equivalent resistance is given by,
$$R_{series}\:=\:R_1\:+\:R_2\:+\:R_3\:+\:\dotsm\:+\:R_n$$
For parallel connection of resistances, the equivalent resistance is,
$$\frac{1}{R_{parallel}}\:=\:\frac{1}{R_1}\:+\:\frac{1}{R_2}\:+\:\frac{1}{R_3}\:+\:\dotsm\:+\frac{1}{R_n}$$
Total voltage or currentAs the resistances in series divides the voltage, thus the total voltage across the series combination is given by,
$$V\:=\:V_1\:+V_2\:+\:\dotsm\:+\:V_n$$
Since the resistances in parallel divides the current in different branches, thus the total current is given by,
$$I\:=\:I_1\:+\:I_2\:+\:\dotsm\:+\:I_n$$
Value of equivalent resistanceAs the resistances in series connection add together, hence the value of equivalent resistance will be greater than the largest resistance.The value of equivalent resistance of a parallel connection of resistances will always be less than the smallest resistance in the combination.
Effect of fault in one resistanceIf a resistance in a series connection breaks down, then the whole circuit will break and the total circuit current will become zero.If a resistance in a parallel connection gets damaged, then it will not affect rest of the resistances, i.e. the current continues to flow through the other resistances.
ApplicationsThe resistances are connected in series to increase the resistance of the circuit to reduce the current according to the load.Resistances are connected in parallel to reduce the total resistance of the circuit. Also, it is used to obtain different currents from a single current.

## Conclusion

The most important difference between resistances in series and resistances in parallel is that the series connection of resistances increases the effective resistance of whole circuit. Whereas, the parallel connection of resistances reduces the effective resistance of the circuit.

Updated on: 04-Jul-2022

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