Lab #6: the LRC Circuit and Resonance: part I

• remember how AC circuits containing caps, inductors, and resistors behave

• experience resonance experimentally

• two week lab. Only 1 lab report. (so, no lab report due next week. A bigish lab report due the following week)

• this week: pgs 56- 57. next week pg 61

LRC Circuit

i

C

Phenomena of resonance an important one in physics

Impedance:Resistor:

Capacitor:

Inductor: i L

R (voltage in phase with current)

(voltage lags current by 90o)

(voltage leads current by 90o)

Current

0

0

0

2 2

( )

1( ( ))

1( )

i t

i t

iV e IR I I i L

CV

I eR i L

CV

I

R LC

I is max when denominator is min: when L=1/C

0

1

LC

Resonance

Resonance

R max

02

/

1 / (width of resonance, V =V / 2)

L R

LQ

R C

phases0

( )0

0

2 2

( )

1( ( ))

1( )

1

tan

i t

i t i t

iV e IR I I i L

CV

I e I eR i L

CV

I

R LC

LC

R

Phase of current (and thus voltage across R) with respect to V0

Phase shift between voltage across resistor and input is zero when at resonant frequency

phases

Note that since VL leads by 90 degrees and Vc lags by 90 degrees, they are always out-of-phase by 180 degrees

IMPORTANT!!!!!

Replace C-1 with

Vary the input frequency using the following values:

(f=f0x(0.1,0.5,0.9,1.0,1.1,1.5,1.9,2.3)

For each value, record the amplitudes of V0 and VR as well as the frequency f and the phase shift phi (from the time shift of the peaks) between V0 and VR. Calculate XL=L and XC=1/C using the measured values for L and C.

Hints• part A1. 200 mH: make this by putting 2 100 mH inductors in series

• Part A1. assume the uncertainty on internal resistance of the waveform generator is 2 ohms. (50+-2)

• C-1 at low frequency, wave form can be ugly. Measure to the average over the “features”. So, need to use cursors, not “measure”

• C-1 don’t assume V0 does not change, monitor it and check that it does not change

• C-1 note phase shift changes sign.

Lab Exam

• Dec 3,4

• The question bank is attached to the web page for this class

Step-wave input

2 20 2

2

1osc

L

R

Charge on cap rings at resonant frequency while decaying away

Like striking a bell with a hammer

At large RCritically damped: R is large enough so that no oscillation occurs

22

4 1

1

LR

C

Hints

• Capture a wave form of the ringing with wavestar

• for part C, only vary R and only give a qualitative answer