# 4.4 Resistors in series and parallel

 Page 1 / 17
• Draw a circuit with resistors in parallel and in series.
• Calculate the voltage drop of a current across a resistor using Ohm’s law.
• Contrast the way total resistance is calculated for resistors in series and in parallel.
• Explain why total resistance of a parallel circuit is less than the smallest resistance of any of the resistors in that circuit.
• Calculate total resistance of a circuit that contains a mixture of resistors connected in series and in parallel.

Most circuits have more than one component, called a resistor    that limits the flow of charge in the circuit. A measure of this limit on charge flow is called resistance    . The simplest combinations of resistors are the series and parallel connections illustrated in [link] . The total resistance of a combination of resistors depends on both their individual values and how they are connected.

## Resistors in series

When are resistors in series    ? Resistors are in series whenever the flow of charge, called the current    , must flow through devices sequentially. For example, if current flows through a person holding a screwdriver and into the Earth, then ${R}_{1}$ in [link] (a) could be the resistance of the screwdriver’s shaft, ${R}_{2}$ the resistance of its handle, ${R}_{3}$ the person’s body resistance, and ${R}_{4}$ the resistance of her shoes.

[link] shows resistors in series connected to a voltage    source. It seems reasonable that the total resistance is the sum of the individual resistances, considering that the current has to pass through each resistor in sequence. (This fact would be an advantage to a person wishing to avoid an electrical shock, who could reduce the current by wearing high-resistance rubber-soled shoes. It could be a disadvantage if one of the resistances were a faulty high-resistance cord to an appliance that would reduce the operating current.)

To verify that resistances in series do indeed add, let us consider the loss of electrical power, called a voltage drop    , in each resistor in [link] .

According to Ohm’s law    , the voltage drop, $V$ , across a resistor when a current flows through it is calculated using the equation $V=\text{IR}$ , where $I$ equals the current in amps (A) and $R$ is the resistance in ohms $\left(\Omega \right)$ . Another way to think of this is that $V$ is the voltage necessary to make a current $I$ flow through a resistance $R$ .

So the voltage drop across ${R}_{1}$ is ${V}_{1}={\mathit{IR}}_{1}$ , that across ${R}_{2}$ is ${V}_{2}={\mathit{IR}}_{2}$ , and that across ${R}_{3}$ is ${V}_{3}={\mathit{IR}}_{3}$ . The sum of these voltages equals the voltage output of the source; that is,

$V={V}_{1}+{V}_{2}+{V}_{3}.$

This equation is based on the conservation of energy and conservation of charge. Electrical potential energy can be described by the equation $\text{PE}=\text{qV}$ , where $q$ is the electric charge and $V$ is the voltage. Thus the energy supplied by the source is $\text{qV}$ , while that dissipated by the resistors is

${\text{qV}}_{1}+{\text{qV}}_{2}+{\text{qV}}_{3}.$

## Connections: conservation laws

The derivations of the expressions for series and parallel resistance are based on the laws of conservation of energy and conservation of charge, which state that total charge and total energy are constant in any process. These two laws are directly involved in all electrical phenomena and will be invoked repeatedly to explain both specific effects and the general behavior of electricity.

#### Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
what is the stm
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?
what is a peer
What is meant by 'nano scale'?
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
what is Nano technology ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
hi
Loga
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!