RC Circuits: Switches, Capacitor Discharge, Time Constant, Decay, and Charging, Slides of Physics

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RC Circuits

Switches

A circuit can be open or closed.

-^

Different states at different times

A switch controls whether a circuit is open or closed.

The schematic symbol is an angled line showing a breakin the circuit.

Time Constant

RC

Q

I









The voltage and current in adischarging capacitor falls withtime.

-^

Fractional change is the same

-^

Never reaches zero



The period of time for adecrease by a factor of

e

is the

time constant



.

Q 

I







RC





Exponential Decay



The discharge of a capacitorcan be represented by anexponential curve.

-^

Depends on initial voltage

/

0

) (

t

e

V

t

V





/

0

) (

t

e

Q C

t

V









/ 0 / 0 ) ( t

t^

e

Q RC

e

V R

t

I









Charging Up



A battery can be used tocharge a capacitor.

-^

Includes resistance



The circuit forms one loop.



The capacitor approaches amaximum voltage.

-^

V = Q/C

R

I(

t)

C

(^

C V R t I V

R

e V R

V

V

t

C



/

V

^

 /

t

C

e

V

V





Charge and Discharge

The curves for charging voltage increases while thecurrent decreases.

When potentials match there is no current.