# A few questions about AC Circuits

Part A - Series RLC Circuit 1st. Get a Q-factor from the measured voltages at resonance; I know the general formula for Q=1/R*sqrt(L/C) L is 4.7 mH and C is 0.01 microF. R is 100 ohm. If I get Q from the general formula, I get Q to be around 6.9. If I try a formula I found online to use voltages at resonance (in this case VC=VL=3.04), I get Q=VC/V. Since V is 1Vrms, I get 1=3.04/sqrt2 which is not near 6.9. Why? How can I calculate Q from the measured voltages? Also, resonancy frequency is 23215 Hz.

Why is there a difference between the values? I assume there were mistakes while doing the experiment, but how can I know which one is more accurate?

Part 2 Series R with parallel LC Values of L and C are the same. R is 100 ohm. Voltage source is 1.5Vrms

1: How do I do a current versus frequency graphic for the parallel circuit? I know that the current entering the parallel must be equal to the one leaving for the series circuit (kirchoff's laws). Should I just get the current at VR and use it as the total current of the circuit?

2: How do I calculate an impedance of LC at resonance?This I really don't know how to do it and found no help online :(

Frequency (calculated by me) is 23.215 kHz, $\omega L$ = 685.6 ohms, current is 10mA therefore voltage across L is 6.856 volts.

This means Q is the same because Q = $\dfrac{\omega L}{R}$ and at resonance this is $\dfrac{1}{R}\sqrt{\dfrac{L}{C}}$.

You have made a mistake somewhere for part A. Maybe your resistor was 200 ohms?

Use the current thru the 100 ohm resistor and bear in mind at resonance the current should be zero because, at resonance, a parallel LC has infinite impedance. You know this because the two currents are exactly equal and opposite (180 degrees apart), therefore current into the parallel LC MUST ALWAYS be zero at resonance. Clearly this long term and not transient analysis of things.

• How did you get the current to be 10mA? No, resistor for A is 100 ohms. Part B The current thru the 1200 ohm is 1.5Vrms*1200? So I=2545A? I'm confused like hell in part B – Roberto Sousa Nov 11 '15 at 22:24
• 1 volt? where did you get that? Shouldn't be square root of 2 because it's 1Vrms? – Roberto Sousa Nov 11 '15 at 22:37
• LC impedances cancel at resonance hence current is 1 v divided by 100 ohms. – Andy aka Nov 11 '15 at 22:38
• You said 1 volt RMS in the question. – Andy aka Nov 11 '15 at 22:39
• Yes, V=1Vrms. But Vrms=Vp/square root of 2. Isn't the V=Vp? – Roberto Sousa Nov 11 '15 at 22:40