Everything Science Grade 11

CHAPTER 19. ELECTRIC CIRCUITS 19.4

19.4 Series and parallelnetworks of resistors

ESBIN

Now that you know howto handle simple seriesand parallel circuits, youare ready to tackle

problems like this:

R 1

R 2

R 3

R 4

R 5

R 6

R 7

Parallel Circuit 1

Parallel Circuit 2

Figure 19.1: An example of a series-parallel network. The dashed boxes indicate parallel sections of

the circuit.

It is relatively easy to work out these kind of circuits because you use everything you have already

learnt about series and parallel circuits. The onlydifference is that you doit in stages. In Figure 19.1,

the circuit consists of 2parallel portions that arethen in series with 1 resistor. So, in order to work out

the equivalent resistance, you start by calculatingthe total resistance of the parallel portions and then

add up all the resistances in series. If all the resistors in Figure 19.1 had resistances of 10 Ω, we can

calculate the equivalentresistance of the entire circuit.

We start by calculating the total resistance of Parallel Circuit 1.

Rp 1

R 4

R 5

R 6

R 7

The value of Rp 1 is:

1

Rp 1

=

1

R 1

+

1

R 2

+

1

R 3

Rp 1 =

�

1

10

+

1

10

+

1

10

�− 1

=

�

1 + 1 + 1

10

�− 1

=

�

3

10

�− 1

= 3,33Ω