Lab Final Exam

• The question bank is posted on the ELMS site under “Final Exam” in “Assignments”

Lab #6: the LRC Circuit and Resonance

• Remember how AC circuits containing a cap, an inductor, and a resistor in series behave

• Measure a resonance experimentally

• Upload a spreadsheet today. A full lab report due by 2 PM same day next week

Crystal radio (AM radio)Where is the crystal? No longer in there. Modern crystal radios use diodes instead.

Today: inductor and capacitor together.

Today: inductor and capacitor together.

AM operates from 535 to 1605 kHz.AM operates from 535 to 1605 kHz.

Series LRC Circuit

The phenomenon of resonance is important in physics

Impedance:Resistor:

Capacitor:

Inductor:

R (voltage in phase with current)

(voltage lags current by 90o)

(voltage leads current by 90o)

Current in the circuit

Current I is max when denominator is min: when ωL=1/ωC

Start with a statement of Kirchoff’s law:

Resonance

Resonance

phases

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

statement of Kirchoff’s law:

phases

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

Hints• part A1. 200 mH: make this by putting two 100 mH inductors in series. Because the mutual inductance is non-negligible, please be sure to wire them together, measure the inductance, and then put them into the circuit wired exactly as when you measured them.

• Part A2. assume the uncertainty on internal resistance of the waveform generator is 2 Ohms. (50 ± 2)

• C-1 at low frequency, the waveform can be ugly. Measure to the average over the “features”. In other words, use cursors, not “measure” on the oscilloscope.

• C-1 don’t assume that V0 is the same at all frequencies, monitor it and record the values.

• C-1 note that the phase shift changes sign as a function of frequency!

Some Derivatives

Step-wave inputCharge 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

Hints

• Capture a wave form of the ringing with wavestar

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