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If two household lightbulbs rated 60 W and 100 W are connected in series to household power, which will be brighter? Explain.

Suppose you are doing a physics lab that asks you to put a resistor into a circuit, but all the resistors supplied have a larger resistance than the requested value. How would you connect the available resistances to attempt to get the smaller value asked for?

Before World War II, some radios got power through a “resistance cord” that had a significant resistance. Such a resistance cord reduces the voltage to a desired level for the radio’s tubes and the like, and it saves the expense of a transformer. Explain why resistance cords become warm and waste energy when the radio is on.

Some light bulbs have three power settings (not including zero), obtained from multiple filaments that are individually switched and wired in parallel. What is the minimum number of filaments needed for three power settings?

Problem exercises

Note: Data taken from figures can be assumed to be accurate to three significant digits.

(a) What is the resistance of ten 275-Ω size 12{"275"- %OMEGA } {} resistors connected in series? (b) In parallel?

(a) 2 . 75 k Ω size 12{2 "." "75"" k" %OMEGA } {}

(b) 27 . 5 Ω size 12{"27" "." 5 %OMEGA } {}

(a) What is the resistance of a 1.00 × 10 2 , a 2 . 50-kΩ , and a 4 . 00-k Ω size 12{4 "." "00""-k" %OMEGA } {} resistor connected in series? (b) In parallel?

What are the largest and smallest resistances you can obtain by connecting a 36 . 0-Ω , a 50 . 0-Ω size 12{"50" "." 0- %OMEGA } {} , and a 700-Ω size 12{"700"- %OMEGA } {} resistor together?

(a) 786 Ω size 12{"786" %OMEGA } {}

(b) 20 . 3 Ω size 12{"20" "." 3 %OMEGA } {}

An 1800-W toaster, a 1400-W electric frying pan, and a 75-W lamp are plugged into the same outlet in a 15-A, 120-V circuit. (The three devices are in parallel when plugged into the same socket.). (a) What current is drawn by each device? (b) Will this combination blow the 15-A fuse?

Your car’s 30.0-W headlight and 2.40-kW starter are ordinarily connected in parallel in a 12.0-V system. What power would one headlight and the starter consume if connected in series to a 12.0-V battery? (Neglect any other resistance in the circuit and any change in resistance in the two devices.)

29 . 6 W size 12{"29" "." 6" W"} {}

(a) Given a 48.0-V battery and 24 . 0-Ω size 12{"24" "." 0- %OMEGA } {} and 96 . 0-Ω size 12{"96" "." 0- %OMEGA } {} resistors, find the current and power for each when connected in series. (b) Repeat when the resistances are in parallel.

Referring to the example combining series and parallel circuits and [link] , calculate I 3 size 12{I rSub { size 8{3} } } {} in the following two different ways: (a) from the known values of I size 12{I} {} and I 2 size 12{I rSub { size 8{2} } } {} ; (b) using Ohm’s law for R 3 size 12{R rSub { size 8{3} } } {} . In both parts explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors .

(a) 0.74 A

(b) 0.742 A

Referring to [link] : (a) Calculate P 3 size 12{P rSub { size 8{3} } } {} and note how it compares with P 3 size 12{P rSub { size 8{3} } } {} found in the first two example problems in this module. (b) Find the total power supplied by the source and compare it with the sum of the powers dissipated by the resistors.

Refer to [link] and the discussion of lights dimming when a heavy appliance comes on. (a) Given the voltage source is 120 V, the wire resistance is 0 . 400 Ω size 12{0 "." "800" %OMEGA } {} , and the bulb is nominally 75.0 W, what power will the bulb dissipate if a total of 15.0 A passes through the wires when the motor comes on? Assume negligible change in bulb resistance. (b) What power is consumed by the motor?

(a) 60.8 W

(b) 3.18 kW

A 240-kV power transmission line carrying 5.00 × 10 2 A is hung from grounded metal towers by ceramic insulators, each having a 1 . 00 × 10 9 size 12{1 "." "00"´"10" rSup { size 8{9} } - %OMEGA } {} resistance. [link] . (a) What is the resistance to ground of 100 of these insulators? (b) Calculate the power dissipated by 100 of them. (c) What fraction of the power carried by the line is this? Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors .

The diagram shows a grounded metal transmission tower. Two ground conductors on top of the tower point out like antennas. Hanging from the tower are a set of three bundled conductors, one on either end and one in the middle.
High-voltage (240-kV) transmission line carrying 5.00 × 10 2 A is hung from a grounded metal transmission tower. The row of ceramic insulators provide 1.00 × 10 9 Ω size 12{1 "." 0 times "10" rSup { size 8{9} } %OMEGA } {} of resistance each.

Show that if two resistors R 1 size 12{R rSub { size 8{1} } } {} and R 2 size 12{R rSub { size 8{2} } } {} are combined and one is much greater than the other ( R 1 >> R 2 size 12{R rSub { size 8{1} } ">>"R rSub { size 8{2} } } {} ): (a) Their series resistance is very nearly equal to the greater resistance R 1 size 12{R rSub { size 8{1} } } {} . (b) Their parallel resistance is very nearly equal to smaller resistance R 2 size 12{R rSub { size 8{2} } } {} .

(a) R s = R 1 + R 2 R s R 1 R 1 >> R 2 alignl { stack { size 12{R rSub { size 8{s} } =R rSub { size 8{1} } +R rSub { size 8{2} } } {} #drarrow R rSub { size 8{s} } »R rSub { size 8{1} } left (R rSub { size 8{1} } ">>"R rSub { size 8{2} } right ) {} } } {}

(b) 1 R p = 1 R 1 + 1 R 2 = R 1 + R 2 R 1 R 2 size 12{ { {1} over {R rSub { size 8{p} } } } = { {1} over {R rSub { size 8{1} } } } + { {1} over {R rSub { size 8{2} } } } = { {R rSub { size 8{1} } +R rSub { size 8{2} } } over {R rSub { size 8{1} } R rSub { size 8{2} } } } } {} ,

so that

R p = R 1 R 2 R 1 + R 2 R 1 R 2 R 1 = R 2 R 1 >> R 2 . alignl { stack { size 12{R rSub { size 8{p} } = { {R rSub { size 8{1} } R rSub { size 8{2} } } over {R rSub { size 8{1} } +R rSub { size 8{2} } } } » { {R rSub { size 8{1} } R rSub { size 8{2} } } over {R rSub { size 8{1} } } } } {} #=R rSub { size 8{2} } left (R rSub { size 8{1} } ">>"R rSub { size 8{2} } right ) "." {} } } {}

Unreasonable Results

Two resistors, one having a resistance of 1 45 Ω size 12{1"45 " %OMEGA } {} , are connected in parallel to produce a total resistance of 150 Ω size 12{150 %OMEGA } {} . (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Unreasonable Results

Two resistors, one having a resistance of 9 00 kΩ size 12{9"00 k" %OMEGA } {} , are connected in series to produce a total resistance of 0 . 500 MΩ size 12{0 "." "500 M" %OMEGA } {} . (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

(a) - 400 k Ω size 12{ +- "400 k" %OMEGA } {}

(b) Resistance cannot be negative.

(c) Series resistance is said to be less than one of the resistors, but it must be greater than any of the resistors.

Questions & Answers

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
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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Introductory physics - for kpu phys 1100 (2015 edition). OpenStax CNX. May 30, 2015 Download for free at http://legacy.cnx.org/content/col11588/1.13
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