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RESISTOR-CAPACITOR

CIRCUITS

christopher e

neil chen

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CIRCUIT

a path between two or more points along which an electrical current can be carried

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CAPACITOR

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an electrical component which stores electric charge

Unlike a battery (which does not store electric charge)

A battery generates a voltage by a chemical reaction to drive electrons through an external circuit. This is the basis of a battery. The battery will continue to provide power until all the reagents have been used up and the reaction stops.

A capacitor is completely different. It has a potential only because charge has been stored on it, and when you connect the capacitor to an external circuit a current only flows until all the charge has drained. Unlike a battery, the voltage on a capacitor is variable and is proportional to the amount of charge stored on it.

(pass around the capacitor) The main application for supercapacitors is in storing and releasing energy, like batteries, which are their main competition. While supercaps can’t hold as much energy as an equally sized battery, they can release it much faster, and they usually have a much longer lifespan.

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CAPACITORS

try to maintain constant voltage;

store energy in an electric field

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CAPACITOR THEORY

HOW DO CAPACITORS WORK?

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CAPACITOR THEORY

HOW DO CAPACITORS WORK?

+

-

electric field

+V

-V

electric potential difference

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V

R

I

CAPACITANCE

the ability of a capacitor to store charge

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CAPACITANCE

the ability of a capacitor to store charge

Q

V

C

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Q

V

C

charge

(coulombs)

capacitance

(farads)

voltage

(volts)

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Q

V

C

charge

(coulombs)

capacitance

(farads)

voltage

(volts)

Q=CV

C=Q/V

V=Q/C

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charging

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V_s

= V_s

fully charged

V_c

diagram with values and everything

Here is a description of how a capacitor stores electrical energy. If we connect the two plates to a battery in a circuit, the battery will drive charges around the circuit as an electric current. When the charges reach the plates they can’t go any further because of the insulating gap so they collect on the plates, one plate becoming positively charged and the other negatively charged. This slow buildup of electric charge actually begins to resist the addition of more charge as a voltage begins to build across the plates, thus opposing the action of the battery. As a consequence, the current flowing in the circuit gets less and less (i.e. it decays), falling to zero when the “back-voltage” on the capacitor is exactly equal and opposite to the battery voltage.

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-

+V_c

-V_c

-

electric potential difference

+

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fully discharged

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CAPACITOR AND RESISTOR�IN SEPARATE LOOPS

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CAPACITOR AND RESISTOR�IN SERIES

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q

t

q=CV_s

V_c=0, q=0

CHARGING A CAPACITOR

|

|�

|

equilibrium charge

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TIME CONSTANT

τ

the amount of time required for a capacitor to accumulate 63.2% of its equilibrium charge

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τ=RC

time constant = resistance × capacitance

(seconds) (ohms) (farads)

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q

t

CHARGING A CAPACITOR

|

|�

|

equilibrium charge

|

q₀

63%

τ=RC

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STEADY STATE PERIOD

5τ

the time period required for a capacitor to become fully charged (reach equilibrium charge)

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|

q

t

CHARGING A CAPACITOR

|

|�

|

equilibrium charge

|

q₀

63%

τ=RC

5τ

steady state

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V_c

V_s

t

RC

voltage across the capacitor

supply voltage (battery voltage)

time elapsed with

supplied voltage

time constant (τ)