Understanding RC Circuits: Voltage, Capacitance, and Resistance, Slides of Physics

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Direct

‐current

circuits

continued

Voltage,

resistor,

and

capacitor

circuits

From

webassign:

I

I^1

eq

R

I

I

I

I

R

V

I

R

I E

E

E

find

to

many ways

the

among

1 1

1

1 1

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C

‐Q

+Q

I

dQ^ dt

I

IR

Q C 







0

Q

RC

dQ dt

R

dQ dt

Q C

1

0

 







What

are

the

units

of

RC?

A.

Seconds B.

Cycles

per

second

C.

Meters D.

Coulombs E.

Volts

t

t

M

r M dMdt

rM

dMdt

at time

money

) (

decrease of

rate

money of n

accumlatio of

rate

:

decrease

for

equation

rate

Simple



 



 

^

 0

0

0

0

) (

)

ln(

)

ln(

:

Analysis

t t r

t t

M M

e M

t M

rt

M

rdt

M

d

dMM

rM

dMdt

           

C

‐Q

+Q

I^ 





/

0

) (

1

1

t t e Q t Q

Q

Q

RC

dQ dt



 

 

e ‐^3

e ‐^2

e ‐^1

Charging

capacitor:

Switch

closed

at

t=0;

Q(t=0)=

^

^

^

^



/

1

) (

1

1

t e

C

t Q

C

Q

C

Q

RC

dQ dt

 



     

E

E

E

Discharging

capacitor

When

switch

closed

Q(t

)=Cc

E

^



/

) (

1

1

t^ c t

e

C

t

Q

Q

Q

RC

dQ dt



 

 

E

a^

b

t

E Q C I /R E

Example

Assume

the

capacitor

is

initially

uncharged.

I

What

is

the

current

I

flowing

through

the

battery

just

when

the

switch

is

closed?

A.

B.

E

/2R

C.

E

/R

D.

E

/R

What

is

the

current

I^

flowing

through

the

battery

after

the

switch

has

been

closed

for

a

long

time?

A.

B.

E

/2R

C.

E

/R

D.

E

/R

When

switch

is

closed

(reset

t=0):

+Q ‐Q

I^2

I^1











/

2

/

2

0

2

/

0

2

2 1 2 1

and

) ( 0 0

t

t

t

e R

e

C

dQ dt

I

C

Q

C R

e Q

t Q

dQdt

I

R I

Q C

R I





     





















E

E

E

E

I^ S

/

2

1

2

2 1

1

0

:

switch

rough

Current th

t

S

S

e R R I I I

I

I

I

















E

E

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