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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)

Test prep for ap courses

A battery is connected to a resistor and an uncharged capacitor. The switch for the circuit is closed at t = 0 s.

  1. While the capacitor is being charged, which of the following is true?

    1. Current through and voltage across the resistor increase.
    2. Current through and voltage across the resistor decrease.
    3. Current through and voltage across the resistor first increase and then decrease.
    4. Current through and voltage across the resistor first decrease and then increase.
  2. When the capacitor is fully charged, which of the following is NOT zero?

    1. Current in the resistor.
    2. Voltage across the resistor.
    3. Current in the capacitor.
    4. None of the above.
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An uncharged capacitor C is connected in series (with a switch) to a resistor R 1 and a voltage source E . Assume E = 24 V, R 1 = 1.2 kΩ and C = 1 mF.

  1. What will be the current through the circuit as the switch is closed? Draw a circuit diagram and show the direction of current after the switch is closed. How long will it take for the capacitor to be 99% charged?
  2. After full charging, this capacitor is connected in series to another resistor, R 2 = 1 kΩ. What will be the current in the circuit as soon as it’s connected? Draw a circuit diagram and show the direction of current. How long will it take for the capacitor voltage to reach 3.24 V?

(a) 20 mA, [link] , 5.5 s; (b) 24 mA, [link] , 2 s

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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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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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