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RLC Circuit
AP Physics C
Mrs. Coyle
RLC circuit
• In real circuits, there is some resistance, and some
energy is lost to internal energy for the resistor
(heat).
• (Some energy is also lost to radiation but this is
ignored).
• Therefore the total energy of the circuit decreases
over time similar to damping in a mass-spring
system.
• Assume the capacitor is
Remember:LC Circuits
initially charged and then the
switch is closed
• Assume no resistance (no
internal energy loss) and no
energy losses to radiation
• The total energy of this system
is constant
2
Q
1 2
U  UC  UL 
 LI
2C 2
Simulation
http://phet.colorado.edu/en/simulation/circu
it-construction-kit-ac
RLC Circuit



The capacitor is charged with the
switch at position a.
At time t = 0, the switch is moved
to position b to form the RLC
circuit.
Kirchhoff’s loop rule:
q
dI
dq
 L  IR  0, and
I
C
dt
dt
d 2 q R dq
1
2
2

  q  0, and  
2
dt
L dt
LC
RLC Circuit
q  Qmax e

R
t
2L
I  Qmax e

1
R
cos d t  , with  

LC 2 L
R
t
2L
2
d
R


d sin d t   2 L cos d t 