<< 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

newtons third law of motion
Nomvulah Reply
how to deal with newtons third law of motion
help me with Newtons laws of universal gravitation
Ntsako Reply
Every particle in the universe attract every other particle with a force that is directly proportional to the product of their mass and inversely proportional to the square of distance between them
guys plz help me how to calculate net force?
Thabiso Reply
its FN +Fg+ Ff+ Ft+Fapplied = Net Force or any force acting on that object
net force is all the forces acting on an Object that is your FN +FG even T +fy or fx anyforce that will act on the object
What's Newton second law
Newton's second law...is when resultant/net force acts on an object,the object will accelerate in the direction of the force at an acceleration directly proportional to the force and inversely proportional to the mass of the object
How do yu calculate normal force on a inclined
net force are FORCES that ACT on that object resultant is a direction or u can say it a magnitude
Newton's second law : the resultant/net force act on an object is equal to the rate of change in momentum.
guys what is the most effective way to know the law of gravitation
any one who can help me with chemistry
george Reply
Yeah Sure. I will help
OK first can you pls teach me how to to calculate on chemistry chapter
What is a derivative?
Hydrocarbon derivatives are compounds that are made primarily of carbon and hydrogen atoms with specific groups of atoms attached. These specific groups of atoms are called functional groups. Hydrocarbon derivatives contain at least one element that is electronegative.
How to find the integral of a specific function?
how do u calculate the mass of an object if u have been given the gradient of a graph?
Hlelelwe Reply
what is endothermic reaction
Mphumuzi Reply
what is the difference between intramolecular and intermolecular forces
Xiluva Reply
please help me here how do the molecular masses of the compounds change?
Khutso Reply
how to calculate atom mass
Mbali Reply
how do water molecules form
Mukonazwothe Reply
water molecules consist of two atoms of hydrogen linked by covalent bonding to the same atom of oxygen ...hydrogen bonds are formed easily when two water molecules come close together , but are easily broken when the water molecule moves apart again
similarity between vander waals forces and hydrogen bond
Angel Reply
type of intermolecular forces between 2 hydrogen and 2 oxygen
when an atom X of an element in Group 1 reacts to become X+
Rhulani Reply
You have O.5 dm^3 of a KNO3 solution of concentration 0.2 M .You need to dilute this solution to get a solution of concentration 0.18M. calculate how many cubic cm of H2O you need to achieve this
Thimna Reply
im really struggling with this question please help me
I don't know how to help i nee you help
what is a radium
Zieniengie Reply
when 3.22 moles ofAl react with 4.96 moles HBr, how many moles of H2 are formed?
Devina Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now

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?