# 4.6 Dc circuits containing resistors and capacitors  (Page 5/9)

 Page 5 / 9

When is the potential difference across a capacitor an emf?

Only when the current being drawn from or put into the capacitor is zero. Capacitors, like batteries, have internal resistance, so their output voltage is not an emf unless current is zero. This is difficult to measure in practice so we refer to a capacitor’s voltage rather than its emf. But the source of potential difference in a capacitor is fundamental and it is an emf.

## Phet explorations: circuit construction kit (dc only)

An electronics kit in your computer! Build circuits with resistors, light bulbs, batteries, and switches. Take measurements with the realistic ammeter and voltmeter. View the circuit as a schematic diagram, or switch to a life-like view.

## Section summary

• An $\text{RC}$ circuit is one that has both a resistor and a capacitor.
• The time constant $\tau$ for an $\text{RC}$ circuit is $\tau =\text{RC}$ .
• When an initially uncharged ( ${V}_{0}=0$ at $t=0$ ) capacitor in series with a resistor is charged by a DC voltage source, the voltage rises, asymptotically approaching the emf of the voltage source; as a function of time,
$V=\text{emf}\left(1-{e}^{-t/\text{RC}}\right)\text{(charging).}$
• Within the span of each time constant $\tau$ , the voltage rises by 0.632 of the remaining value, approaching the final voltage asymptotically.
• If a capacitor with an initial voltage ${V}_{0}$ is discharged through a resistor starting at $t=0$ , then its voltage decreases exponentially as given by
$V={V}_{0}{e}^{-t/\text{RC}}\text{(discharging).}$
• In each time constant $\tau$ , the voltage falls by 0.368 of its remaining initial value, approaching zero asymptotically.

## Conceptual questions

Regarding the units involved in the relationship $\tau =\text{RC}$ , verify that the units of resistance times capacitance are time, that is, $\Omega \cdot F=s$ .

The $\text{RC}$ time constant in heart defibrillation is crucial to limiting the time the current flows. If the capacitance in the defibrillation unit is fixed, how would you manipulate resistance in the circuit to adjust the $\text{RC}$ constant $\tau$ ? Would an adjustment of the applied voltage also be needed to ensure that the current delivered has an appropriate value?

When making an ECG measurement, it is important to measure voltage variations over small time intervals. The time is limited by the $\text{RC}$ constant of the circuit—it is not possible to measure time variations shorter than $\text{RC}$ . How would you manipulate $R$ and $C$ in the circuit to allow the necessary measurements?

Draw two graphs of charge versus time on a capacitor. Draw one for charging an initially uncharged capacitor in series with a resistor, as in the circuit in [link] , starting from $\text{t}=0$ . Draw the other for discharging a capacitor through a resistor, as in the circuit in [link] , starting at $\text{t}=0$ , with an initial charge ${Q}_{0}$ . Show at least two intervals of $\tau$ .

When charging a capacitor, as discussed in conjunction with [link] , how long does it take for the voltage on the capacitor to reach emf? Is this a problem?

When discharging a capacitor, as discussed in conjunction with [link] , how long does it take for the voltage on the capacitor to reach zero? Is this a problem?

Referring to [link] , draw a graph of potential difference across the resistor versus time, showing at least two intervals of $\tau$ . Also draw a graph of current versus time for this situation.

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
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
has a lot of application modern world
Kamaluddeen
yes
narayan
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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