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Equivalent resistance of two parallel resistor, R p

For 2 resistors in parallel with resistances R 1 and R 2 , the equivalent resistance is:

R p R 1 R 2 R 1 R 2

Equivalent parallel resistance

Consider a circuit consisting of a single cell and three resistors that are connected in parallel.

Using what we know about voltage and current in parallel circuits we can define the equivalent resistance of several resistors in parallel as:

Equivalent resistance in a parallel circuit, R p

For n resistors in parallel, the equivalent resistance is:

1 R p = 1 R 1 + 1 R 2 + 1 R 3 + + 1 R n

Let us apply this formula to the following circuit.

What is the total resistance in the circuit?

1 R p = 1 R 1 + 1 R 2 + 1 R 3 = 1 10 Ω + 1 2 Ω + 1 1 Ω = 1 + 5 + 10 10 = 16 10 R p = 0 , 625 Ω

Experiment : current in parallel circuits

Aim:

To determine the effect of multiple resistors on current in a circuit

Apparatus:

  • Battery
  • Resistors
  • Light bulb
  • Wires

Method:

  1. Construct the following circuits
  2. Rank the three circuits in terms of the brightness of the bulb.

Conclusions:

The brightness of the bulb is an indicator of how much current is flowing. If the bulb gets brighter because of a change then more current is flowing. If the bulb gets dimmer less current is flowing. You will find that the more resistors you have the brighter the bulb.

Why is this the case? Why do more resistors make it easier for charge to flow in the circuit? It is because they are in parallel so there are more paths for charge to take to move. You can think of it like a highway with more lanes, or the tube of marbles splitting into multiple parallel tubes. The more branches there are, the easier it is for charge to flow. You will learn more about the total resistance of parallel resistors later but always remember that more resistors in parallel mean more pathways. In series the pathways come one after the other so it does not make it easier for charge to flow.

Two 8 k Ω resistors are connected in parallel. Calculate the equivalent resistance.

  1. Since the resistors are in parallel we can use:

    1 R p = 1 R 1 + 1 R 2
  2. 1 R p = 1 R 1 + 1 R 2 = 1 8 k Ω + 1 10 k Ω R p = 2 8 = 4 k Ω
  3. The equivalent resistance of two 8 k Ω resistors connected in parallel is 4 k Ω .

Two resistors are connected in parallel. The equivalent resistance is 100 Ω . If one resistor is 150 Ω , calculate the value of the second resistor.

  1. Since the resistors are in parallel we can use:

    1 R p = 1 R 1 + 1 R 2

    We are given the value of R p and R 1 .

  2. 1 R p = 1 R 1 + 1 R 2 1 R 2 = 1 R p - 1 R 1 = 1 100 Ω - 1 150 Ω = 3 - 2 300 = 1 300 R 2 = 300 Ω
  3. The second resistor has a resistance of 300 Ω .

Khan academy video on circuits - 3

Resistance

  1. What is the unit of resistance called and what is its symbol?
  2. Explain what happens to the total resistance of a circuit when resistors are added in series?
  3. Explain what happens to the total resistance of a circuit when resistors are added in parallel?
  4. Why do batteries go flat?

Khan academy video on circuits - 4

The following presentation summarizes the concepts covered in this chapter.

Exercises - electric circuits

  1. Write definitions for each of the following:
    1. resistor
    2. coulomb
    3. voltmeter
  2. Draw a circuit diagram which consists of the following components:
    1. 2 batteries in parallel
    2. an open switch
    3. 2 resistors in parallel
    4. an ammeter measuring total current
    5. a voltmeter measuring potential difference across one of the parallel resistors
  3. Complete the table below:
    Quantity Symbol Unit of meaurement Symbol of unit
    e.g. Distance e.g. d e.g. kilometer e.g. km
    Resistance
    Current
    Potential difference
  4. Draw a diagram of a circuit which contains a battery connected to a lightbulb and a resistor all in series.
    1. Also include in the diagram where you would place an ammeter if you wanted to measure the current through the lightbulb.
    2. Draw where and how you would place a voltmeter in the circuit to measure the potential difference across the resistor.
  5. Thandi wants to measure the current through the resistor in the circuit shown below and sets up the circuit as shown below. What is wrong with her circuit setup?
  6. [SC 2003/11] The emf of a battery can best be explained as the
    1. rate of energy delivered per unit current
    2. rate at which charge is delivered
    3. rate at which energy is delivered
    4. charge per unit of energy delivered by the battery
  7. [IEB 2002/11 HG1] Which of the following is the correct definition of the emf of a battery?
    1. It is the product of current and the external resistance of the circuit.
    2. It is a measure of the cell's ability to conduct an electric current.
    3. It is equal to the “lost volts” in the internal resistance of the circuit.
    4. It is the power supplied by the battery per unit current passing through the battery.
  8. [IEB 2005/11 HG] Three identical light bulbs A, B and C are connected in an electric circuit as shown in the diagram below.
    1. How bright is bulb A compared to B and C?
    2. How bright are the bulbs after switch S has been opened?
    3. How do the currents in bulbs A and B change when switch S is opened?
      Current in A Current in B
      (a) decreases increases
      (b) decreases decreases
      (c) increases increases
      (d) increases decreases
  9. [IEB 2004/11 HG1] When a current I is maintained in a conductor for a time of t , how many electrons with charge e pass any cross-section of the conductor per second?
    1. It
    2. It/e
    3. Ite
    4. e/It

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
The fundamental frequency of a sonometer wire streached by a load of relative density 's'are n¹ and n² when the load is in air and completly immersed in water respectively then the lation n²/na is
Mukesh Reply
Properties of longitudinal waves
Sharoon Reply

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Source:  OpenStax, Siyavula textbooks: grade 10 physical science [caps]. OpenStax CNX. Sep 30, 2011 Download for free at http://cnx.org/content/col11305/1.7
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