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RC Circuits for timing

RC size 12{ ital "RC"} {} circuits are commonly used for timing purposes. A mundane example of this is found in the ubiquitous intermittent wiper systems of modern cars. The time between wipes is varied by adjusting the resistance in an RC size 12{ ital "RC"} {} circuit. Another example of an RC size 12{ ital "RC"} {} circuit is found in novelty jewelry, Halloween costumes, and various toys that have battery-powered flashing lights. (See [link] for a timing circuit.)

A more crucial use of RC size 12{ ital "RC"} {} circuits for timing purposes is in the artificial pacemaker, used to control heart rate. The heart rate is normally controlled by electrical signals generated by the sino-atrial (SA) node, which is on the wall of the right atrium chamber. This causes the muscles to contract and pump blood. Sometimes the heart rhythm is abnormal and the heartbeat is too high or too low.

The artificial pacemaker is inserted near the heart to provide electrical signals to the heart when needed with the appropriate time constant. Pacemakers have sensors that detect body motion and breathing to increase the heart rate during exercise to meet the body’s increased needs for blood and oxygen.

Part a shows a charging circuit containing cell of e m f script E connected to a resistor R and capacitor C and a closed switch to complete the circuit. The current is shown to flow clockwise through this arm of the circuit alone. A bulb of high resistance R is connected across the capacitor. Part b shows a discharging circuit containing a cell of e m f script E connected to a resistor R and capacitor C and a closed switch to complete the circuit. A bulb of low resistance R is connected across the capacitor. Current flows clockwise through the arm containing the capacitor and the low resistance bulb. Part c is a graph showing variation of voltage verses time for the bulb in above circuit. The voltage is plotted along the vertical axis and the time is plotted along the horizontal axis. The curve has a smooth rise from the origin, reaches a plateau at threshold value of voltage where it begins to drop and rise as a small sawtooth wave with maxima lying along the threshold line.
(a) The lamp in this RC size 12{ ital "RC"} {} circuit ordinarily has a very high resistance, so that the battery charges the capacitor as if the lamp were not there. When the voltage reaches a threshold value, a current flows through the lamp that dramatically reduces its resistance, and the capacitor discharges through the lamp as if the battery and charging resistor were not there. Once discharged, the process starts again, with the flash period determined by the RC size 12{ ital "RC"} {} constant τ size 12{τ} {} . (b) A graph of voltage versus time for this circuit.

Calculating time: RC Circuit in a heart defibrillator

A heart defibrillator is used to resuscitate an accident victim by discharging a capacitor through the trunk of her body. A simplified version of the circuit is seen in [link] . (a) What is the time constant if an 8.00-μF size 12{8 "." "00"-mF} {} capacitor is used and the path resistance through her body is 1.00 × 10 3 Ω ? (b) If the initial voltage is 10.0 kV, how long does it take to decline to 5.00 × 10 2 V ?


Since the resistance and capacitance are given, it is straightforward to multiply them to give the time constant asked for in part (a). To find the time for the voltage to decline to 5.00 × 10 2 V , we repeatedly multiply the initial voltage by 0.368 until a voltage less than or equal to 5.00 × 10 2 V is obtained. Each multiplication corresponds to a time of τ size 12{τ} {} seconds.

Solution for (a)

The time constant τ size 12{τ} {} is given by the equation τ = RC size 12{τ= ital "RC"} {} . Entering the given values for resistance and capacitance (and remembering that units for a farad can be expressed as s / Ω size 12{s/ %OMEGA } {} ) gives

τ = RC = ( 1.00 × 10 3 Ω ) ( 8 . 00 μF ) = 8 . 00 ms. size 12{τ= ital "RC"= \( "1000" %OMEGA \) \( 8 "." "00" μF \) =8 "." "00"" ms"} {}

Solution for (b)

In the first 8.00 ms, the voltage (10.0 kV) declines to 0.368 of its initial value. That is:

V = 0 . 368 V 0 = 3.680 × 10 3 V at  t = 8 . 00 ms. size 12{t=8 "." "00"" ms"} {}

(Notice that we carry an extra digit for each intermediate calculation.) After another 8.00 ms, we multiply by 0.368 again, and the voltage is

V = 0.368 V = 0.368 3.680 × 10 3 V = 1.354 × 10 3 V at t = 16.0 ms.

Similarly, after another 8.00 ms, the voltage is

V ′′ = 0.368 V = ( 0.368 ) ( 1.354 × 10 3 V ) = 498 V at t = 24 .0 ms.


So after only 24.0 ms, the voltage is down to 498 V, or 4.98% of its original value. Such brief times are useful in heart defibrillation, because the brief but intense current causes a brief but effective contraction of the heart. The actual circuit in a heart defibrillator is slightly more complex than the one in [link] , to compensate for magnetic and AC effects that will be covered in Magnetism .

Questions & Answers

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 to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
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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
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
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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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