# Measuring Voltage across Resistor in Series RLC Circuit

1. Feb 22, 2016

### SataSata

I was experimenting with resonant frequency of a series RLC circuit:

5V AC source
10 ohms resistor
100microF capacitor
46mH inductor

Resonant frequency is calculated to be around 74.2Hz. So I set the AC source to resonant frequency 74.2Hz and measured the voltage across the 10 ohms resistor using an oscilloscope. I was expecting to measure close to source voltage of 5V. However I got only 1.34V. That's a phase angle of around 74.4 degrees instead of 0.

If my theory is correct, I should get 5V since impedance is minimum with only the resistance 10 ohms as inductance and capacitance "balance out".
The connections are straightforward and shouldn't have any mis-connection and the AC source has the right voltage and frequency as seen on the oscilloscope. I'm curious as to what possible errors or factors that I might had missed and hope you guys can enlightenment me if I misunderstood something. Thank you.

2. Feb 22, 2016

### Svein

I suspect that your 100μF capacitor is an electrolytic. This means:
1. The capacitor needs a DC potential across it in order to work.
2. Even if the capacitor is correctly biased, the usual tolerance for an electrolytic is "+100% to -50%"

3. Feb 22, 2016

### Hesch

I think you have forgotten that there is some resistance in the inductor as well.

Try to measure this resistance and recalculate.

4. Feb 22, 2016

### lychette

Did you alter the frequency around 74Hz and check for resonanc?...the voltage across the resistor would be a maximum at resonance.
The 'missing'3.66 volts could easily be due to resistance of the inductor.

5. Feb 22, 2016

### jim hardy

see if this lessens the confusion
use two voltmeters
tune frequency for maximum voltage across the inductor and capacitor
when they're equal you're resonant

6. Feb 23, 2016

### lychette

If the inductor has significant resistance this will not be accurate?
At resonance the current is max in a series circuit and a good way to detect this is to measure the voltage across the series resistance. At resonance this should equal the supply voltage. If it is not equal to the supply voltage this indicates there is more series resistance somewhere! In this example I think it is the inductor.

7. Feb 23, 2016

### jim hardy

What you say is quite correct.
He can easily measure the resistance of his inductor with an ohm-meter
The capacitor also has some internal resistance. That is more difficult to measure.

What is important is to get him to take some more measurements, thinking about their meaning as he goes along.

Why i suggested two meters is it should drive home for him that the circuit shifts from inductive to capacitive around resonance.

That's a really good observation !

8. Feb 23, 2016

### SataSata

Thank you everybody for the help. It turns out the inductor indeed has a resistance of 20+ ohms and is consistent with the measured voltage across the resistor. Again, thank you very much.

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