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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.

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Phet explorations: circuit construction kit (dc only)

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Circuit Construction Kit (DC only)

Section summary

  • An RC size 12{ ital "RC"} {} circuit is one that has both a resistor and a capacitor.
  • The time constant τ size 12{τ} {} for an RC size 12{ ital "RC"} {} circuit is τ = RC size 12{τ= ital "RC"} {} .
  • When an initially uncharged ( V 0 = 0 size 12{V rSub { size 8{0} } =0} {} at t = 0 size 12{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 = emf ( 1 e t / RC ) (charging). size 12{V="emf" \( 1 - e rSup { size 8{ - t/ ital "RC"} } \) } {}
  • Within the span of each time constant τ size 12{τ} {} , the voltage rises by 0.632 of the remaining value, approaching the final voltage asymptotically.
  • If a capacitor with an initial voltage V 0 size 12{V rSub { size 8{0} } } {} is discharged through a resistor starting at t = 0 size 12{t=0} {} , then its voltage decreases exponentially as given by
    V = V 0 e t / RC (discharging). size 12{V=V rSub { size 8{0} } e rSup { size 8{ - t/ ital "RC"} } \) } {}
  • In each time constant τ size 12{τ} {} , the voltage falls by 0.368 of its remaining initial value, approaching zero asymptotically.

Conceptual questions

Regarding the units involved in the relationship τ = RC size 12{τ= ital "RC"} {} , verify that the units of resistance times capacitance are time, that is, Ω F = s size 12{ %OMEGA cdot F=s} {} .

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The RC size 12{ ital "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 RC size 12{ ital "RC"} {} constant τ size 12{τ} {} ? Would an adjustment of the applied voltage also be needed to ensure that the current delivered has an appropriate value?

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When making an ECG measurement, it is important to measure voltage variations over small time intervals. The time is limited by the RC size 12{ ital "RC"} {} constant of the circuit—it is not possible to measure time variations shorter than RC size 12{ ital "RC"} {} . How would you manipulate R size 12{R} {} and C size 12{C} {} in the circuit to allow the necessary measurements?

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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 t = 0 size 12{t=0} {} . Draw the other for discharging a capacitor through a resistor, as in the circuit in [link] , starting at t = 0 size 12{t=0} {} , with an initial charge Q 0 size 12{Q rSub { size 8{0} } } {} . Show at least two intervals of τ size 12{τ} {} .

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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?

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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?

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Referring to [link] , draw a graph of potential difference across the resistor versus time, showing at least two intervals of τ size 12{τ} {} . Also draw a graph of current versus time for this situation.

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Questions & Answers

A soccer player kicked off a ball at velocity of 62 ft/s at angle 45°. A goal keeper is 43 yard away from the direction in which ball kicked off. At what minimum velocity he runs to meet the ball?
Ram Reply
A soccer player kicked off the ball at the velocity of 62 ft/s at 45° with horizontal.A goal keeper is 43 yard away from the ball kicked position.At what minimum velocity he runs to meet the ball?
Ram
what is torque
Deepak Reply
The turning effect of force is called torque.
Uzair
What is the effect of static electricity
Ruth
what there factors affect the surface tension of a liquid
Promise Reply
formula for impedance
muyiwa Reply
ehat is central forces
Nita Reply
what is distance?
Jonathan Reply
What does mean ohms law imply
Victoria Reply
ohms law state that the electricity passing through a metallic conductor is directly proportional to the potential difference across its end
muyiwa
what is matter
folajin Reply
Anything that occupies space
Kevin
Any thing that has weight and occupies space
Victoria
Anything which we can feel by any of our 5 sense organs
Suraj
Right
Roben
thanks
Suraj
what is a sulphate
Alo
any answers
Alo
the time rate of increase in velocity is called
Blessing Reply
acceleration
Emma
What is uniform velocity
Victoria
Greetings,users of that wonderful app.
Frank Reply
how to solve pressure?
Cruz Reply
how do we calculate weight and eara eg an elefant that weight 2000kg has four fits or legs search of surface eara is 0.1m2(1metre square) incontact with the ground=10m2(g =10m2)
Cruz
P=F/A
Mira
can someone derive the formula a little bit deeper?
Bern
what is coplanar force?
OLADITI Reply
forces acting and lying on d same plane
Promise
what is accuracy and precision
Peace Reply
How does a current follow?
Vineeta Reply
follow?
akif
which one dc or ac current.
akif
how does a current following?
Vineeta
?
akif
AC current
Vineeta
AC current follows due to changing electric field and magnetic field.
akif
you guys are just saying follow is flow not follow please
Abubakar
ok bro thanks
akif
flows
Abubakar
but i wanted to understand him/her in his own language
akif
but I think the statement is written in English not any other language
Abubakar
my mean that in which form he/she written this,will understand better in this form, i write.
akif
ok
Abubakar
ok thanks bro. my mistake
Vineeta
u are welcome
Abubakar
what is a semiconductor
Vineeta Reply
substances having lower forbidden gap between valence band and conduction band
akif
what is a conductor?
Vineeta
replace lower by higher only
akif
convert 56°c to kelvin
Abubakar
How does a current follow?
Vineeta
A semiconductor is any material whose conduction lies between that of a conductor and an insulator.
AKOWUAH
Practice Key Terms 3

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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