# 4.6 Dc circuits containing resistors and capacitors  (Page 6/9)

 Page 6 / 9

A long, inexpensive extension cord is connected from inside the house to a refrigerator outside. The refrigerator doesn’t run as it should. What might be the problem?

In [link] , does the graph indicate the time constant is shorter for discharging than for charging? Would you expect ionized gas to have low resistance? How would you adjust $R$ to get a longer time between flashes? Would adjusting $R$ affect the discharge time?

An electronic apparatus may have large capacitors at high voltage in the power supply section, presenting a shock hazard even when the apparatus is switched off. A “bleeder resistor” is therefore placed across such a capacitor, as shown schematically in [link] , to bleed the charge from it after the apparatus is off. Why must the bleeder resistance be much greater than the effective resistance of the rest of the circuit? How does this affect the time constant for discharging the capacitor?

## Problem exercises

The timing device in an automobile’s intermittent wiper system is based on an $\text{RC}$ time constant and utilizes a $0\text{.}\text{500-μF}$ capacitor and a variable resistor. Over what range must $R$ be made to vary to achieve time constants from 2.00 to 15.0 s?

$\text{range 4}\text{.}\text{00 to 30}\text{.}\text{0 M}\Omega$

A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance?

The duration of a photographic flash is related to an $\text{RC}$ time constant, which is $0\text{.}\text{100 μs}$ for a certain camera. (a) If the resistance of the flash lamp is $0\text{.}\text{0400}\phantom{\rule{0.15em}{0ex}}\Omega$ during discharge, what is the size of the capacitor supplying its energy? (b) What is the time constant for charging the capacitor, if the charging resistance is $\text{800}\phantom{\rule{0.25em}{0ex}}\text{kΩ}$ ?

(a) $2\text{.}\text{50 μF}$

(b) 2.00 s

A 2.00- and a $7\text{.}\text{50-μF}$ capacitor can be connected in series or parallel, as can a 25.0- and a $\text{100-kΩ}$ resistor. Calculate the four $\text{RC}$ time constants possible from connecting the resulting capacitance and resistance in series.

After two time constants, what percentage of the final voltage, emf, is on an initially uncharged capacitor $C$ , charged through a resistance $R$ ?

86.5%

A $\text{500-Ω}$ resistor, an uncharged $1\text{.}\text{50-μF}$ capacitor, and a 6.16-V emf are connected in series. (a) What is the initial current? (b) What is the $\text{RC}$ time constant? (c) What is the current after one time constant? (d) What is the voltage on the capacitor after one time constant?

A heart defibrillator being used on a patient has an $\text{RC}$ time constant of 10.0 ms due to the resistance of the patient and the capacitance of the defibrillator. (a) If the defibrillator has an $8\text{.}\text{00-μF}$ capacitance, what is the resistance of the path through the patient? (You may neglect the capacitance of the patient and the resistance of the defibrillator.) (b) If the initial voltage is 12.0 kV, how long does it take to decline to $6.00×{10}^{2}\phantom{\rule{0.25em}{0ex}}\text{V}$ ?

(a) $1\text{.}\text{25 k}\Omega$

(b) 30.0 ms

An ECG monitor must have an $\text{RC}$ time constant less than $1.00×{10}^{2}\phantom{\rule{0.25em}{0ex}}\text{μs}$ to be able to measure variations in voltage over small time intervals. (a) If the resistance of the circuit (due mostly to that of the patient’s chest) is $1\text{.}00 k\Omega$ , what is the maximum capacitance of the circuit? (b) Would it be difficult in practice to limit the capacitance to less than the value found in (a)?

[link] shows how a bleeder resistor is used to discharge a capacitor after an electronic device is shut off, allowing a person to work on the electronics with less risk of shock. (a) What is the time constant? (b) How long will it take to reduce the voltage on the capacitor to 0.250% (5% of 5%) of its full value once discharge begins? (c) If the capacitor is charged to a voltage ${V}_{0}$ through a $\text{100-Ω}$ resistance, calculate the time it takes to rise to $0\text{.}\text{865}{V}_{0}$ (This is about two time constants.)

(a) 20.0 s

(b) 120 s

(c) 16.0 ms

Using the exact exponential treatment, find how much time is required to discharge a $\text{250-μF}$ capacitor through a $\text{500-Ω}$ resistor down to 1.00% of its original voltage.

Using the exact exponential treatment, find how much time is required to charge an initially uncharged 100-pF capacitor through a $\text{75}\text{.}0\text{-M}\Omega$ resistor to 90.0% of its final voltage.

$1\text{.}\text{73}×{\text{10}}^{-2}\phantom{\rule{0.25em}{0ex}}\text{s}$

Integrated Concepts

If you wish to take a picture of a bullet traveling at 500 m/s, then a very brief flash of light produced by an $\text{RC}$ discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one $\text{RC}$ constant is acceptable, and given that the flash is driven by a $\text{600-μF}$ capacitor, what is the resistance in the flash tube?

$3\text{.}\text{33}×{\text{10}}^{-3}\phantom{\rule{0.25em}{0ex}}\Omega$

Integrated Concepts

A flashing lamp in a Christmas earring is based on an $\text{RC}$ discharge of a capacitor through its resistance. The effective duration of the flash is 0.250 s, during which it produces an average 0.500 W from an average 3.00 V. (a) What energy does it dissipate? (b) How much charge moves through the lamp? (c) Find the capacitance. (d) What is the resistance of the lamp?

Integrated Concepts

A $\text{160-μF}$ capacitor charged to 450 V is discharged through a $31\text{.}\text{2-k}\Omega$ resistor. (a) Find the time constant. (b) Calculate the temperature increase of the resistor, given that its mass is 2.50 g and its specific heat is $1\text{.}\text{67}\frac{\text{kJ}}{\text{kg}\phantom{\rule{0.15em}{0ex}}\cdot \phantom{\rule{0.15em}{0ex}}\text{ºC}}$ , noting that most of the thermal energy is retained in the short time of the discharge. (c) Calculate the new resistance, assuming it is pure carbon. (d) Does this change in resistance seem significant?

(a) 4.99 s

(b) $3\text{.}\text{87ºC}$

(c) $\text{31}\text{.}\text{1 k}\Omega$

(d) No

Unreasonable Results

(a) Calculate the capacitance needed to get an $\text{RC}$ time constant of $1.00×{10}^{3}\phantom{\rule{0.25em}{0ex}}\text{s}$ with a $0\text{.}\text{100-Ω}$ resistor. (b) What is unreasonable about this result? (c) Which assumptions are responsible?

Consider a camera’s flash unit. Construct a problem in which you calculate the size of the capacitor that stores energy for the flash lamp. Among the things to be considered are the voltage applied to the capacitor, the energy needed in the flash and the associated charge needed on the capacitor, the resistance of the flash lamp during discharge, and the desired $\text{RC}$ time constant.

Consider a rechargeable lithium cell that is to be used to power a camcorder. Construct a problem in which you calculate the internal resistance of the cell during normal operation. Also, calculate the minimum voltage output of a battery charger to be used to recharge your lithium cell. Among the things to be considered are the emf and useful terminal voltage of a lithium cell and the current it should be able to supply to a camcorder.

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
what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Got questions? Join the online conversation and get instant answers!