Lab 7: RLC Resonant CircuitsOnly 5 more labs to go!!

C

L

When we connect a charged capacitor to an inductor oscillationswill occur in the charge of the capacitor and the current throughthe inductor.

Energy stored in the capacitor before the switch is closed:

Switch

When the switch is closed, charge flows (current) through the inductor.

2

2

1CVE

The current through the inductor will continue to flow until an energy equal to:

2

2

1LIE

This energy is storedin the magnetic field of the inductor.

Current continuesto flow and thecapacitor becomes charged againbut with opposite polarity

This energy exchange between the capacitorand inductor is similar to that of a mass spring system:

QCAP X

IL V

Just like the mass-spring system has a frequency of oscillation,

the current and charge in the LC circuit will oscillate with a frequency:

LCf

2

1

m

kf

2

1

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 frictionin the mass-spring oscillating system.

When a resistor is added to the circuit the resonant frequency becomes:

NOTE: What is the units fromL x C = Henry x Farad = seconds2

2

222

2

12

24

11

4

1

2

1

2

1

L

R

CLf

L

R

LCf

NOTE: When R 0, f reduces to:LC

f2

1

2

222

2

12

24

11

4

1

2

1

2

1

L

R

CLf

L

R

LCf

f2

1/C

0

bmxy

slopeL

Lslope

22 4

1

4

1

2

2 24

1

L

Rb