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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)

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.

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

Two bodies P and Quarter each of mass 1000g. Moved in the same direction with speed of 10m/s and 20m/s respectively. Calculate the impulse of P and Q obeying newton's 3rd law of motion
Shimolla Reply
definition for wave?
Doc Reply
A disturbance that travel from one medium to another and without causing permanent change to its displacement
Fagbenro
In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport (Mass transfer). ... There are two main types ofwaves: mechanical and electromagnetic. Mechanicalwaves propagate through a physical matter, whose substance is being deformed
Devansh
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Thanks
AMADI
Note: LINEAR MOMENTUM Linear momentum is defined as the product of a system’s mass multiplied by its velocity: size 12{p=mv} {}
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Study of matter and energy
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physics is the science of matter and energy and their interactions
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31. Calculate the initial (from rest) acceleration of a proton in a 5.00×106 N/C electric field (such as created by a research Van de Graaff). Explicitly show how you follow the steps in the Problem-Solving Strategy for electrostatics.
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A tennis ball is projected at an angle and attains a range of 78. if the velocity is 30metres per second, calculate the angle
Shimolla
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Wisdom Reply
question on friction
Wisdom
the rubbing of one object or surface against another.
author
momentum is the product of mass and it's velocity.
Algayawi
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Edina
Friction is a force that exist between two objects in contact. e.g. friction between road and car tires.
Eklu
With regards to a shielded cable, is there an induced current on the shield when the center conductor is carrying an AC Current? What is the formula?
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Force is the cause and momentum is its effect.
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A force is a pull or a push on an object, causing an object to move or a moving object to stop.
Eklu
Find the velocity that make one full oscillation in 10 seconds and also makes 1.7meters in the same time
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Oluwaseun
17m/s
Eklu
17m/s
Gabriel
0.17
Devansh
17m/s
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Acquah
t=10s a=1.7m v=? u=0 but v=u+at but u=0 v=at 1.7×10=17 v=17m/s that's how I solved it.
Eklu
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Acquah
How is a=1.7m?
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a is an acceleration
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Doc
its relating to time and oscillation made.
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You mean A as an amplitude?
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A voltmeter is a device use in measuring electric potential in a volt.
Ahmad
Find out the equation of a simple harmonic progressive wave that have 0.2m with a frequency of 550hertz.If the wave moves along a positive x axis with the speed of 330m/s
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principle is a guiding belief Law is authority or instruction
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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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