Chapter 31: RLC Circuits
Chapter 31: RLC Circuits
PHY2049: Chapter 31
1
Topics
?LC Oscillations
Conservation of energy
?Damped oscillations in RLC circuits
Energy loss
?AC current
RMS quantities
?Forced oscillations
Resistance, reactance, impedance Phase shift Resonant frequency Power
?Transformers
Impedance matching
PHY2049: Chapter 31
2
LC Oscillations
?Work out equation for LC circuit (loop rule) - q - L di = 0 C dt
CL
?Rewrite using i = dq/dt
L
d 2q dt 2
+
q C
=
0
d 2q dt 2
+
2q
=
0
= 1
LC
(angular frequency) has dimensions of 1/t
?Identical to equation of mass on spring
m
d2x dt 2
+
kx
=
0
d2x dt 2
+
2
x
=
0
= k
m
PHY2049: Chapter 31
3
LC Oscillations (2)
?Solution is same as mass on spring oscillations
q = qmax cos(t + )
= k
m
qmax is the maximum charge on capacitor is an unknown phase (depends on initial conditions)
?Calculate current: i = dq/dt
i = -qmax sin (t + ) = -imax sin (t + )
?Thus both charge and current oscillate
Angular frequency , frequency f = /2 Period: T = 2/ Current and charge differ in phase by 90?
PHY2049: Chapter 31
4
Plot Charge and Current vs t
q = qmax cos(t ) i = -imax sin (t )
t
PHY2049: Chapter 31
5
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