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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

Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
Widad Reply
can you send the book attached ?
Ariel
?
Ariel
What is economics
Widad Reply
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn Reply
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn
what is ecnomics
Jan Reply
this is the study of how the society manages it's scarce resources
Belonwu
what is macroeconomic
John Reply
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
etc
husaini
difference between firm and industry
husaini Reply
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from Qd  120 3P to Qd  90  3P and the supply function has shifted from QS  20  2P to QS 10  2P . a) Find the effect of this change on price and quantity. b) Which of the changes in demand and supply is higher?
Toofiq Reply
explain standard reason why economic is a science
innocent Reply
factors influencing supply
Petrus Reply
what is economic.
Milan Reply
scares means__________________ends resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Zarshad Reply
Why qualify 28 supplies
Milan
what are explicit costs
Nomsa Reply
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
David Reply
economic overview notes
Amahle Reply
identify a demand and a supply curve
Salome Reply
i don't know
Parul
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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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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