<< Chapter < Page Chapter >> Page >

Series and parallel networks of resistors

Now that you know how to handle simple series and parallel circuits, you are ready to tackle problems like this:

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 only difference is that you do it in stages. In [link] , the circuit consists of 2 parallel portions that are then in series with 1 resistor. So, in order to work out the equivalent resistance, you start by calculating the total resistance of the parallel portions and then add up all the resistances in series. If all the resistors in [link] had resistances of 10  Ω , we can calculate the equivalent resistance of the entire circuit.

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

The value of R p 1 is:

1 R p 1 = 1 R 1 + 1 R 2 + 1 R 3 R p 1 = 1 10 + 1 10 + 1 10 - 1 = 1 + 1 + 1 10 - 1 = 3 10 - 1 = 3 , 33 Ω

We can similarly calculate the total resistance of Parallel Circuit 2 :

1 R p 2 = 1 R 5 + 1 R 6 + 1 R 7 R p 2 = 1 10 + 1 10 + 1 10 - 1 = 1 + 1 + 1 10 - 1 = 3 10 - 1 = 3 , 33 Ω

This has now being simplified to a simple series circuit and the equivalent resistance is:

R = R p 1 + R 4 + R p 2 = 10 3 + 10 + 10 3 = 100 + 30 + 100 30 = 230 30 = 7 , 66 Ω

The equivalent resistance of the circuit in [link] is 7,66 Ω .

Series and parallel networks

Determine the equivalent resistance of the following circuits:

Wheatstone bridge

Another method of finding an unknown resistance is to use a Wheatstone bridge . A Wheatstone bridge is a measuring instrument that is used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. Its operation is similar to the original potentiometer except that in potentiometer circuits the meter used is a sensitive galvanometer.

Interesting fact

The Wheatstone bridge was invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843.

In the circuit of the Wheatstone bridge, R x is the unknown resistance. R 1 , R 2 and R 3 are resistors of known resistance and the resistance of R 2 is adjustable. If the ratio of R 2 : R 1 is equal to the ratio of R x : R 3 , then the voltage between the two midpoints will be zero and no current will flow between the midpoints. In order to determine the unknown resistance, R 2 is varied until this condition is reached. That is when the voltmeter reads 0 V.

What is the resistance of the unknown resistor R x in the diagram below if R 1 =4 Ω   R 2 =8 Ω and R 3 =6 Ω .

  1. The arrangement is a Wheatstone bridge. So we use the equation:

    R x : R 3 = R 2 : R 1
  2. R x : R 3 = R 2 : R 1 R x : 6 = 8 : 4 R x = 12 Ω
  3. The resistance of the unknown resistor is 12  Ω .

Got questions? Get instant answers now!

Power in electric circuits

In addition to voltage and current, there is another measure of free electron activity in a circuit: power . Power is a measure of how rapidly a standard amount of work is done. In electric circuits, power is a function of both voltage and current:

Electrical Power

Electrical power is calculated as:

P = I · V

Questions & Answers

what is the relationship between the strength of intermolecular Force and boiling point
Onias Reply
what is atom?
Ice_ Reply
what is Boyle's law
Nqabisa Reply
what is field
Opara Reply
am I cuutee? ahhh uhh ahjk
Pogo Reply
hey Pride
Matema
hey l am tatenda mativenga
Lynn
hey Tatenda and Pride
Akhona
I'm good thanks and you?
Akhona
Hi wasup in here
eugenia
good idea
Khayalethu
I am not doing gr 11 but I'm helping gr11 learner
Lwanele
that good we do need people with more knowledge in gr11 science work
Sfundo
Thanks for helping us
Puleng
hi
Gauss
hi gyz
Nqabisa
Hi guys
Mr
Hello I'm Trudy Allowance Ndlovu
Trudy Reply
hi Trudy
Akhona
konichiwa
Pogo
hello Trudy
Matema
Hi I'm Thantsha
Thantsha
hy trudy
Khayalethu
hi am Puleng
Puleng
great thanks and u
Puleng
I am also doing Physics
Mzikazi
yes
Puleng
hi guyz
Christine
I'm so very impressed this apps
Christine
yeah
Puleng
Assalamu Alaikum everyone 😍
Sheikh
interesting
Gauss
Hii guys I'm David Kekana Can we do a study group 👥
Mr
what is a test charge n how do u determine the direction of of electric strength on a point
Khayalethu Reply
what is intermolecular forces
Mandy Reply
type of intermolecular force
Mandy
Are forces that act between stable molecules And we have two type's of intermolecular forces * polar and non-polar
Mr
what is intramolecular force
Thantsha Reply
what are the bonding atom
datuali Reply
what is atom
datuali
fused atom
Alyssa
building blocks of matter
Alyssa
Hey Alyssa!
Sheikh
who brought obout the gas law
Dennis Reply
what do you think will happen to semi metal when place in boiling water
Dennis
dill ute
Alyssa
?
Alyssa
how does the molecular shape influences the boiling point and melting point of molecules?
Itumeleng Reply
how is transverse wave different from longitudinal wave
maneo Reply
Transverse waves move perpendicular to the surface... and longitudinal waves move parallel to the surface. Does it make sense to u?
McDonald
yes thank you
maneo
your welcome... where do u stay?
McDonald
Lesotho
maneo
yeah
Alyssa
ur tens Maneo pls
McDonald
what is the formula to calculate a longitudinal wave
Keaton Reply
what is Snell's law
Leekat Reply
Snell's law (also known as Snell-Descarteslaw and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, air.
Jhandy

Get the best Siyavula textbooks: gr... course in your pocket!





Source:  OpenStax, Siyavula textbooks: grade 11 physical science. OpenStax CNX. Jul 29, 2011 Download for free at http://cnx.org/content/col11241/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: grade 11 physical science' conversation and receive update notifications?

Ask