Parallel & Series Resistors: calculations & formulas

Description of the way resistors can be placed in series and parallel to make other resistance values.

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Resistors can be placed in many configurations in an electrical or electronic circuit.

In some instances the resistors may be placed in series, whereas in others they may be placed in parallel.

When they are placed in these configurations it is important to be able to calculate the overall resistance. This can be achieved quite easily when the right formulas are used - there are simple formulas for both series and parallel resistors.

Resistors in series

If the resistors are placed in series then the overall resistance is simply the sum of the individual resistors.

Resistors in series
Resistors in series

This can be expressed mathematically as follows:

Rtotal = R 1 + R 2 + R 3 + . . . . . .

As an example, if three resistors having values of 1 kohm, 2 kohm and 3 kohm are placed in series then the total resistance is 1 + 2 + 3 kohm = 6 kohm.

Resistors in parallel

If resistors are placed in parallel they share the current and the situation is a little more difficult to calculate, but still quite easy.

Resistors in parallel
1 Rtotal = 1 R1 + 1 R2 + 1 R3 + . . . . . .

To give an example if there are three resistors in parallel with values of 1 kohm, 2 kohm and 3 kohm then the overall value of the combination can be worked out:

1/R Total     =     1/1000     +     1/2000     +     1/3000

1/R Total     =     1/1000     +     1/2000     +     1/3000

1/R Total     =     6/6000     +     3/6000     +     2/6000

1/R Total     =     11/6000

R Total    =     6000/11 ohms or 545 ohms

Case of only two resistors in parallel

Sometimes this can be rather tedous to calculate. Fortunately when there are only two resistors in parallel the formula simplifies to:

Two resistors in parallel
R total = R 1 R 2 R 1 + R 2

This formula really simplifies the calculation of the value of two resistors in parallel.

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