Series and parallel resistors

- resistors in series and parallel, the formulae, equations or calculations involved.

Resistor networks consisting of resistors in series or resistors in parallel are often found in electronic circuits.

There are many reasons why parallel resistor networks or series resistor networks may be used. It is possible that the required value may not be available, and a combination of two or more may provide the required value. Alternatively using more than one resistor may enable the required overall wattage to be achieved.

These scenarios are often found when manufacturers need to limit the number of different types or values of resistor in a design as this helps reduce costs. In this way, using series or parallel resistor networks may provide significant advantages.


Resistors in series

Resistors can be placed in series or parallel. When placed in series the total resistance is equal to the sum of the individual resistors:

Resistors in series
Resistors in series

 Resistors in series formula and calculation

It is also worth noting that the same current flows through each resistor, but the voltage across each resistor is proportional to the resistance of that particular resistor.


Resistors in parallel

For resistors placed in parallel, the arithmetic is a little more complicated because the reciprocal of the total resistance is equal to the sum of the reciprocals of the constituent resistors:

Resistors in parallel
Resistors in parallel

As the voltage across all the resistors is the same and the current is shared according to the resistance of the individual resistors, the formula for calculating the overall resistance of the resistors in parallel is more complicated than the series resistor case and becomes:

 Resistors in parallel formula and calculation


Two resistors in parallel

In most cases there are only two resistors in a parallel network. Normally it is not necessary to involve more than two resistors.

Resistors in parallel

In this case where there are only two resistors R1 and R2 in parallel the calculation can be simplified.

Two resistors in parallel formula and calculation

If both these resistors have the same value it can be seen that the overall value of the resistance is half the value for the individual resistor.

When resistors are placed in parallel the voltage across the resistors is the same, but the current through each one is inversely proportional to its resistance.


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