Download RC Circuits

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 break
in the circuit.
Capacitor Discharge
I(t)
C
R
 A capacitor stores charge.
• Related to voltage
• Q = CV
• V = Q/C
 A switch can be used to
Q (t )
V (t ) 
C
V (t ) Q(t )
I (t ) 

R
RC
complete a circuit with a
resistor.
• Current in circuit
• Decreases as charge is
removed
Time Constant
 The voltage and current in a
discharging capacitor falls with
time.
• Fractional change is the same
• Never reaches zero
 The period of time for a
decrease by a factor of e is the
time constant t.
Q
I 
RC
I 
Q
t
t  RC
Exponential Decay
 The discharge of a capacitor
can be represented by an
exponential curve.
• Depends on initial voltage
V (t )  V0 e  t /t
Q0 t /t
V (t ) 
e
C
V0 t /t Q0 t /t
I (t )  e

e
R
RC
Capacitor Loop
 A capacitor in a circuit behaves
like a voltage source.
I
C
R
• V = Q/C
• Depends on time
 A loop with a capacitor follows
VC  IR  0
V0 e t /t  IR  0
Kirchhoff’s voltage law.
Charging Up
 A battery can be used to
I(t)
R
charge a capacitor.
• Includes resistance
V
C
 The circuit forms one loop.
 The capacitor approaches a
V  I (t ) R  VC  0
maximum voltage.
• V = Q/C
V

VC  V   e t /t  R
R


VC  V 1  e  t /t

Charge and Discharge
 The curves for charging voltage increases while the
current decreases.
 When potentials match there is no current.