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Lab 7: RLC Resonant Circuits
Only 5 more labs to go!!
L
When we connect a charged capacitor to an inductor oscillations
will occur in the charge of the capacitor and the current through
the inductor.
Energy stored in the capacitor before the switch is closed:
1
E  CV 2
2
When the switch is closed,
charge flows (current)
through the inductor.
Switch
C
This energy exchange
between the capacitor
and inductor is similar
to that of a mass spring
system:
QCAP  X
IL  V
Current continues
to flow and the
capacitor becomes
charged again
but with opposite
polarity
The current through the inductor will
continue to flow until an energy equal to:
1 2
E  LI
2
This energy is stored
in the magnetic field of
the inductor.
Just like the mass-spring system has a frequency of oscillation,
1
f 
2
k
m
the current and charge in the LC circuit will oscillate with a frequency:
f 
1
2 LC
NOTE: What is the units from
L x C = Henry x Farad = seconds2
If we connect a resistor in series with the capacitor and inductor the oscillations will be
damped until the energy stored diminishes to zero. This is similar to if we consider friction
in the mass-spring oscillating system.
When a resistor is added to the circuit the resonant frequency becomes:
1
2
2
2


1 1  R 
1  R 
 1 1
2
f 
    f   2   2  

2  LC  2 L  
 4 L  C 4  2 L 
NOTE: When R 0, f reduces to:
f 
1
2 LC
1
2
2
2


1 1  R 
1  R 
 1 1
2
f 
    f   2   2  

2  LC  2 L  
 4 L  C 4  2 L 
y  mx  b
f2
1
1
slope  2  L  2
4 L
4 slope
0
1  R 
b 2

4  2 L 
2
1/C