# 12.1 Resistors in series and parallel  (Page 8/17)

 Page 8 / 17

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 $\text{275-Ω}$ resistors connected in series? (b) In parallel?

(a) $2\text{.}\text{75}\phantom{\rule{0.25em}{0ex}}\text{k}\Omega$

(b) $\text{27}\text{.}5\phantom{\rule{0.25em}{0ex}}\Omega$

(a) What is the resistance of a $\text{1.00}×{10}^{2}-\Omega$ , a $2\text{.}\text{50-kΩ}$ , and a $4\text{.}\text{00-k}\Omega$ resistor connected in series? (b) In parallel?

What are the largest and smallest resistances you can obtain by connecting a $\text{36}\text{.}0-\Omega$ , a $\text{50}\text{.}0-\Omega$ , and a $\text{700-Ω}$ resistor together?

(a) $\text{786}\phantom{\rule{0.25em}{0ex}}\Omega$

(b) $\text{20}\text{.}3\phantom{\rule{0.25em}{0ex}}\Omega$

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.)

$\text{29}\text{.}6\phantom{\rule{0.25em}{0ex}}\text{W}$

(a) Given a 48.0-V battery and $\text{24}\text{.}0-\Omega$ and $\text{96}\text{.}0-\Omega$ 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 ${I}_{3}$ in the following two different ways: (a) from the known values of $I$ and ${I}_{2}$ ; (b) using Ohm’s law for ${R}_{3}$ . 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 ${P}_{3}$ and note how it compares with ${P}_{3}$ 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 $0\text{.}\text{400}\phantom{\rule{0.25em}{0ex}}\Omega$ , 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 $5.00×{10}^{2}\phantom{\rule{0.25em}{0ex}}\text{A}$ is hung from grounded metal towers by ceramic insulators, each having a $1\text{.}\text{00}×{\text{10}}^{9}-\Omega$ 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 .

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

(a) $\begin{array}{}{R}_{\text{s}}={R}_{1}+{R}_{2}\\ ⇒{R}_{\text{s}}\phantom{\rule{0.25em}{0ex}}\approx \phantom{\rule{0.25em}{0ex}}{R}_{1}\left({R}_{1}\text{>>}{R}_{2}\right)\end{array}$

(b) $\frac{1}{{R}_{p}}=\frac{1}{{R}_{1}}+\frac{1}{{R}_{2}}=\frac{{R}_{1}+{R}_{2}}{{R}_{1}{R}_{2}}$ ,

so that

$\begin{array}{}{R}_{p}=\frac{{R}_{1}{R}_{2}}{{R}_{1}+{R}_{2}}\approx \frac{{R}_{1}{R}_{2}}{{R}_{1}}={R}_{2}\left({R}_{1}\text{>>}{R}_{2}\right)\text{.}\end{array}$

Unreasonable Results

Two resistors, one having a resistance of $1\text{45}\phantom{\rule{0.25em}{0ex}}\Omega$ , are connected in parallel to produce a total resistance of $150\phantom{\rule{0.25em}{0ex}}\Omega$ . (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 $9\text{00 kΩ}$ , are connected in series to produce a total resistance of $0\text{.}\text{500 MΩ}$ . (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

(a) $-\text{400 k}\Omega$

(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.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
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
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
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
Got questions? Join the online conversation and get instant answers!