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 big lab report due the following week) this week: pgs next week pg 61

LRC Circuit Phenomena of resonance an important one in physics Impedence: Resistor: Capacitor: Inductor: R (voltage in phase with current) (voltage lags current by 90 o ) (voltage leads current by 90 o )

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

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

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=WL and XC=1/wC using the measured values for L and C.

Hints part A mH -> 100mH Part A1. assume uncertainty on internal resistanc eof the wave for is 2 ohms. C-1 at low frequency, wave form across inductor is 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. C-3. don’t read off plot. Just extrapolate data linearly between the + and – shift point. ditto for C-4

Step-wave input Charge on cap rings at resonant frequency while decaying away Like striking a bell with a hammer

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

Hints: Part b Capture a wave form of the ringing with wavestar