Resonance not occurring at right frequencies

[samreid]

In slack, Isam said:

I am not sure if I am doing something wrong. I made a circuit with a resistor, one inductor (50 H) and a capacitor (0.1 F) so resonance should be around 0.45 Hz. The largest current I am getting is at the lowest available frequency of 0.1 Hz! Also, when I change the frequency, both current and voltage (I measured voltage on the resistor) jump a bit before settling back to a normal oscillation. Is this natural? (My experience with RLCs is at high frequencies with oscilloscopes.)

Sorry. I get frequency of 0.07 Hz and the dial has 0.1 Hz as the smallest value, so one cannot see the constant voltage at zero hertz.

I also changed the capacitance (I put 2 in series and 2 in parallel). Same result. Max current at 0.1 Hz.

[ariel-phet]

@samreid we do not have a 50 H inductor possible. 10 H is the max. I think Isam may have misread, and it was probably a 5.0 H inductor. Resonance appears to be occurring at the correct frequency still.

[issamali67]

Apologies to re-open this. There is a 50 H inductor (just to check that my eyes are not fooling me, I showed it to my son and it is 50!). This is the default value I get in the prototype. Once I realized that its value is a variable, I played with it and found that the minimum is 10 H. Few comments (based on me teaching college students):

(1) I changed the values of L and C so that I get the largest and smallest resonance frequencies. The max/min are between 0.1 to 0.2 Hz, which is a very small range. I checked the voltage on R at the min frequency and it should be close to zero at f < f_resonance. This is not that clear when f_resonance is small. Ideally, it is a good thing to have f = 0 to see the effect of the capacitor (yes, I do realize this is DC, but it would be nice to see DC as a limit of AC, at least for 1st-year college students). The effect is clearer for f >> f_resonance in this sim. (2) When I change f in "AC Voltage" and "RLC" tabs, the "Voltage chart" jumps a bit before settling back to plotting a normal sine wave. This also occurs in the "Lab" tab. (3) I am not sure how much of real-life you are interested in vs dishing out the concepts to students. Generally, C of 0.1 F or more are large. For most applications the value is in the micro, nano and pico Farads. Inductors are in milli Henries (+/-). But I see why you want large values: because you want to see the oscillations in the voltage and current charts. (4) Some of the important parameters are impedance Z, and V_rms and I_rms. Would it be possible to have a graph of each (or at least I_rms) vs f? This would show the peak at f= f_resonance and the effect of power loss due to R when one changes its value. One can tie this nicely with a forced, damped spring. Same mathematical structure. (5) Would it be possible also to show a phasor diagram rotating? Here one can see the effect of different values of C and L on the circuit phase. The rotation gives the oscillations of the voltages in R, L, C and the current. Bonus: can see the current lagging voltage in L and vise versa in C. To me this is more important than showing the sine curves for V and I (from the conceptual point of view).

By the way, this is a very nice sim.

[arouinfar]

@issamali67 the publically-available prototype is very old and frankly buggy. Can you try out the latest dev version instead? https://phet-dev.colorado.edu/html/circuit-construction-kit-ac/1.0.0-dev.43/phet/circuit-construction-kit-ac_en_phet.html

[issamali67]

Thanks. Will do.

[issamali67]

I looked at this latest prototype. I like this sim. Here are few comments:

(1) You do not need L up to 4 significant figures. Your resonance frequency is within 0.1 Hz accuracy. (2) Same for input voltage, R and C. I think 2 significant figures should be enough. (3) I checked the "RLC" tab and set both L and C values at their smallest (C = 0.05 F, L = 0.1 H). In this case f_resonance = 2.25 Hz, which is beyond the max f of 2 Hz available. I intentionally put V_input = 120 V max and R = 120 ohms. At f < 0.1 Hz, V_resistor should go to zero. This cannot be seen. It would be really nice to see this because it shows the effect of C as open circuit, and one can relate this nicely to DC circuits as a limiting case. (4) Still with "RLC": I set C = 0.2 F and L = 10 H (largest values available). This gives f_resonance = 0.11 Hz. I could not see the change in V_resistor between 0.1 Hz - 1 Hz. Then it starts slowly decreasing by the time I got to 2 Hz. This is because I set R = 120 ohms. At smaller R (I used 3 ohms) the decay is faster. (5) I tried C = 0.1 F and L = 0.8 H so that f_resonance = about 1 Hz. I thought this would enable me to see V_resistor -> 0 at f very small (close to 1 Hz) and f = 2 Hz. But I get 50 V across R. This may lead some students to think that one can still get large V at limiting cases across R (even though 50 V is small compared to V_resistor at resonance). (6) I still get kinks in the V chart when I change f and, depending on values of C and L, it could take a bit longer time for the chart to settle to a nice regular oscillation.

I think, if possible, it would be nice to change the frequency range to start from zero and end, say, at >= 3Hz, so that students can see the limiting behavior at large and small frequencies. From my experience with college students, it was an issue for students to remember the C is open circuit at very small f and L is open at very large L.

In point (4) above, I used a large R and so it was difficult to see the change in V_resistor till I got near 2 Hz. The sharpness of the resonance it interesting in its own right and shows how efficient is the energy transfer in a circuit. I suggest to add an I_rms (or V_rms across R) vs f plot so one can show the effect on R on the sharpness of resonance. Say adding and "advanced" button to get the graph. Can this be done in an animated way? If so, it would be nice to add an additional a "Z" button for impedance to generate a Z vs f graph to see that Z is minimum at resonance and that Z depends on f.

I also suggest to have a phasor diagram. Instructors always draw such diagrams on a white/black board and, naturally, this drawing is static. But in reality these phasors actually rotate with angular speed 2 x pi x f. The nice thing about such diagrams is that they show the phase difference among the various circuit components and each component V with the current through circuit. They also show the phase on the circuit (here is another "phase" button that I suggest to see phase vs f). One can animate the diagram further by changing the values of R, L, C and see how the circuit phase changes due to the change in the magnitudes of the phasors themselves.

I looked at the "Advanced" in the "Lab" tab. There you have wire resistivity and source resistance. If you are concerned with the RLC behavior, then wire and source resistances are just added resistors and they will not add much to the conceptual understanding of the AC circuit. These, in my opinion, are more useful as starting points for electrical circuits in general and they would fit nicely in DC circuits (I think you already have them there but did not check).

[samreid]

There are numerous design recommendations in these comments. @arouinfar can you please review and create side issues as appropriate? If there is a model issue that may be solved with a different circuit solver, please add label "circuit-construction-kit:model".