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.

Remember:LC Circuits• Assume the capacitor is 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

221

2 2IC L

QU U U L

C

Simulation

http://phet.colorado.edu/en/simulation/circuit-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:

0 and q dI dq

L IR , IC dt dt

22 2

2

10 and

d q R dqq ,

dt L dt LC

RLC Circuit

221

with 2

RtL

max d d

Rq Q e cos t ,

LC L

2

2

RtL

max d d d

RI Q e sin t cos t

L