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

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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 $\text{275-Ω}$ 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.

What is the frictional forc e between two bodies
it is the force which always opposes the motion of the body
ZAMAN
what is a wave
wave means. A field of study
aondohemba
what are Atoms
aondohemba
is the movement back and front or up and down
sani
how ?
aondohemba
wave is a disturbance that transfers energy through matter or space with little or no associated mass.
lots
A wave is a motion of particles in disturbed medium that carry energy from one midium to another
conist
an atom is the smallest unit( particle) of an element that bares it's chemical properties
conist
what is electromagnetic induction?
conist
what's boy's law
mahmud
How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?
How do you convert 0.0045kgcmÂ³ to the si unit?
how many state of matter do we really have like I mean... is there any newly discovered state of matter?
I only know 5: •Solids •Liquids •Gases •Plasma •Bose-Einstein condensate
Thapelo
Alright Thank you
Falana
Which one is the Bose-Einstein
James
can you explain what plasma and the I her one you mentioned
Olatunde
u can say sun or stars are just the state of plasma
Mohit
but the are more than seven
Issa
list it out I wanna know
Cristal
what the meaning of continuum
What state of matter is fire
fire is not in any state of matter...fire is rather a form of energy produced from an oxidising reaction.
Xenda
Isn`t fire the plasma state of matter?
Walter
all this while I taught it was plasma
Victor
How can you define time?
Time can be defined as a continuous , dynamic , irreversible , unpredictable quantity .
Tanaya
unpredictable? but I can say after one o'clock its going to be two o'clock predictably!
Victor
how can we define vector
mahmud
I would define it as having a magnitude (size)with a direction. An example I can think of is a car traveling at 50m/s (magnitude) going North (direction)
Hanzo
as for me guys u would say time is quantity that measures how long it takes for a specific condition to happen e.g how long it takes for the day to end or how it takes for the travelling car to cover a km.
conist
what is the relativity of physics
How do you convert 0.0045kgcm³ to the si unit?
flint
What is the formula for motion
V=u+at V²=u²-2as
flint
S=ut+½at
flint
they are eqns of linear motion
King
S=Vt
Thapelo
v=u+at s=ut+at^\2 v^=u^+2as where ^=2
King
hi
hello
King
Explain dopplers effect
Not yet learnt
Bob
Explain motion with types
Bob
Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
Scalar quantity Because acceleration has only magnitude
Bob
acleration is vectr quatity it is found in a spefied direction and it is product of displcemnt
bhat
its a scalar quantity
Paul
velocity is speed and direction. since velocity is a part of acceleration that makes acceleration a vector quantity. an example of this is centripetal acceleration. when you're moving in a circular patter at a constant speed, you are still accelerating because your direction is constantly changing.
Josh
acceleration is a vector quantity. As explained by Josh Thompson, even in circular motion, bodies undergoing circular motion only accelerate because on the constantly changing direction of their constant speed. also retardation and acceleration are differentiated by virtue of their direction in
fitzgerald
respect to prevailing force
fitzgerald
What is the difference between impulse and momentum?
Manyo
Momentum is the product of the mass of a body and the change in velocity of its motion. ie P=m(v-u)/t (SI unit is kgm/s). it is literally the impact of collision from a moving body. While Impulse is the product of momentum and time. I = Pt (SI unit is kgm) or it is literally the change in momentum
fitzgerald
Or I = m(v-u)
fitzgerald
the tendency of a body to maintain it's inertia motion is called momentum( I believe you know what inertia means) so for a body to be in momentum it will be really hard to stop such body or object..... this is where impulse comes in.. the force applied to stop the momentum of such body is impulse..
Pelumi
Calculation of kinetic and potential energy
K.e=mv² P.e=mgh
Malia
K is actually 1/2 mv^2
Josh
what impulse is given to an a-particle of mass 6.7*10^-27 kg if it is ejected from a stationary nucleus at a speed of 3.2*10^-6ms²? what average force is needed if it is ejected in approximately 10^-8 s?
John
speed=velocity÷time velocity=speed×time=3.2×10^-6×10^-8=32×10^-14m/s impulse [I]=∆momentum[P]=mass×velocity=6.7×10^-27×32×10^-14=214.4×10^-41kg/ms force=impulse÷time=214.4×10^-41÷10^-8=214.4×10^-33N. dats how I solved it.if wrong pls correct me.
Melody
what is sound wave
sound wave is a mechanical longitudinal wave that transfers energy from one point to another
Ogor
its a longitudnal wave which is associted wth compresion nad rearfractions
bhat
what is power
it's also a capability to do something or act in a particular way.
Kayode
Newton laws of motion
Mike
power also known as the rate of ability to do work
Slim
power means capabilty to do work p=w/t its unit is watt or j/s it also represents how much work is done fr evry second
bhat