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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 size 12{R} {} to get a longer time between flashes? Would adjusting R size 12{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?

An electrical circuit with a capacitor has an extra resistor R sub b l, called a bleeder, installed in parallel with the capacitor.
A bleeder resistor R bl size 12{R rSub { size 8{"bl"} } } {} discharges the capacitor in this electronic device once it is switched off.

Problem exercises

The timing device in an automobile’s intermittent wiper system is based on an RC size 12{ ital "RC"} {} time constant and utilizes a 0 . 500-μF size 12{0 "." "500-"μF} {} capacitor and a variable resistor. Over what range must R size 12{R} {} be made to vary to achieve time constants from 2.00 to 15.0 s?

range 4 . 00 to 30 . 0 M Ω size 12{"range 4" "." "00 to 30" "." "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 RC size 12{ ital "RC"} {} time constant, which is 0 . 100 μs size 12{0 "." "100" μs} {} for a certain camera. (a) If the resistance of the flash lamp is 0 . 0400 Ω size 12{0 "." "0400" %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 800 size 12{"800"" k" %OMEGA } {} ?

(a) 2 . 50 μF size 12{2 "." "50 "mF} {}

(b) 2.00 s

A 2.00- and a 7 . 50-μF size 12{7 "." "50"-mF} {} capacitor can be connected in series or parallel, as can a 25.0- and a 100-kΩ size 12{"100""-k" %OMEGA } {} resistor. Calculate the four RC size 12{ ital "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 size 12{C} {} , charged through a resistance R size 12{R} {} ?


A 500-Ω size 12{"500"- %OMEGA } {} resistor, an uncharged 1 . 50-μF size 12{1 "." "50"-mF} {} capacitor, and a 6.16-V emf are connected in series. (a) What is the initial current? (b) What is the RC size 12{ ital "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 RC size 12{ ital "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 . 00-μF size 12{8 "." "00"-mF} {} 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 V ?

(a) 1 . 25 k Ω size 12{1 "." "25 k" %OMEGA } {}

(b) 30.0 ms

An ECG monitor must have an RC size 12{ ital "RC"} {} time constant less than 1.00 × 10 2 μs size 12{"100" ms} {} 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 . 00 kΩ size 12{1 "." 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 size 12{V rSub { size 8{0} } } {} through a 100-Ω size 12{"100"- %OMEGA } {} resistance, calculate the time it takes to rise to 0 . 865 V 0 size 12{0 "." "865"`V rSub { size 8{0} } } {} (This is about two time constants.)

A parallel circuit with a switch, an embedded electronic circuit, a capacitor, and a resistor is shown. The embedded circuit, capacitor, and resistor are connected in parallel with each other: the electronic circuit on the left, the capacitor in the middle, and the resistor on the right. The capacitor has a capacitance of eighty micro farads. The resistor has a resistance of two hundred fifty kilohms. The switch is on the top, between the electronic circuit and the capacitor leg.

(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 250-μF size 12{"250"-mF} {} capacitor through a 500-Ω size 12{"500"- %OMEGA } {} 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 75 . 0 -M Ω size 12{"75" "." 0"-M" %OMEGA } {} resistor to 90.0% of its final voltage.

1 . 73 × 10 2 s size 12{1 "." "73" times "10" rSup { size 8{ - 2} } " 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 RC size 12{ ital "RC"} {} discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one RC size 12{ ital "RC"} {} constant is acceptable, and given that the flash is driven by a 600-μF size 12{"600"-mF} {} capacitor, what is the resistance in the flash tube?

3 . 33 × 10 3 Ω size 12{3 "." "33"´"10" rSup { size 8{-3} } %OMEGA } {}

Integrated Concepts

A flashing lamp in a Christmas earring is based on an RC size 12{ ital "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 160-μF size 12{"160"-mF} {} capacitor charged to 450 V is discharged through a 31 . 2-k Ω size 12{31 "." "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 . 67 kJ kg ºC size 12{1 "." "67" { {"kJ"} over {"kg" cdot "deg"C} } } {} , 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 . 87ºC size 12{3 "." "87"°C} {}

(c) 31 . 1 k Ω size 12{"31" "." "1 k" %OMEGA } {}

(d) No

Unreasonable Results

(a) Calculate the capacitance needed to get an RC size 12{ ital "RC"} {} time constant of 1.00 × 10 3 s with a 0 . 100-Ω size 12{0 "." "100"- %OMEGA } {} resistor. (b) What is unreasonable about this result? (c) Which assumptions are responsible?

Construct Your Own Problem

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 RC size 12{ ital "RC"} {} time constant.

Construct Your Own Problem

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.

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Practice Key Terms 3

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Source:  OpenStax, College physics ii. OpenStax CNX. Nov 29, 2012 Download for free at http://legacy.cnx.org/content/col11458/1.2
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