Understanding RLC Circuits & Resonance Lab: Oscilloscopes, Generators, & Multimeters, Lab Reports of Physics

Download Understanding RLC Circuits & Resonance Lab: Oscilloscopes, Generators, & Multimeters and more Lab Reports Physics in PDF only on Docsity! — PHYS 375: Lab 4 – RLC circuits & Resonance – Purposes Get familiar with the usage of an oscilloscope and a function generator. Understand how a digital multimeter works with AC signal. Show that the current flowing in a capacitor is proportional to the time derivative of the voltage across the capacitor. 1 Time domain study of oscillations Build the circuit shown in Figure 1 with L = 1 mH. Setup the signal generator to provide square signals with proper amplitude and frequency to clearly see the signal oscillation due to the RLC circuit: tune f closed to the resonance frequency. R Vg L C Vg Vc Figure 1: Circuit for parts 1 and 2. 1. Take C = 100 nF a vary R from 0 to 5 kΩ, observe, i.e. make a sketch and describe, the different oscillatory regimes. For R = 0, the oscillation are still damped why? 2. For R = 0, measure the oscillation period, T0, for C=11,27, 51.1, 100, 220, 470 nF. Plot ω0 ≡ 2π/T versus C and superimpose the theoretically expected curve. 3. For each of the previously use capacitor value, vary R and find out the critical resistance (corresponding to the critical damping regime). Plot R versus C and superimpose the theoretically expected curve. 4. For the case C = 100 nF measure the amplitudes of consecutive oscillation maxima Un, Un+1 (see Figure 2) and using the formula δ = 1/T0 log[Un/Un+1] compute the damping constant δ. 1 V c time U n U n+1 T 0 Figure 2: Definition of the period and consecutive amplitudes for the estimation of damping constant δ. 2 Resonance Consider the same circuit as built in the previous section but setup the signal generator to produce a sinusoidal wave. Use a capacitor with capacitance C = 11 nF. 1. For different values of R approximately corresponding to quality factor of Q = 0.1, 1, 2, and 5: (a) vary the frequency of the sinusoidal signal, (b) for each frequency setting, measure the voltage across the capacitor Vc and the tension produced by the frequency generator Vg (the oscilloscope will be used in ”standard” mode), (c) compute the ratio T (f) ≡ Vc/Vg, (d) switch the oscilloscope to X-Y mode you should see an ellipse, (e) measure the phase between the two signal Φ(f) (see section 3). 2. For the four cases of resistance values, corresponding to Q = 0.1, 1, 2, and 5, plot the curves T (ω) and Φ(ω) as a function of ω/ω0 [ω0 is the resonance frequency of the circuit that you can compute knowing L and C]. 2