Determine resonant frequency of an AC voltage source

[AndrejN96]

Homework Statement

Given a series RLC circuit, with one R, one L, and one C element, and an AC voltage source with variable frequency, find the resonant frequency experimentally given an ammeter and a voltmeter.

Homework Equations

The current in the circuit when the circuit is in resonance is maximum.
The imaginary part of the total impedance/admittance of the circuit is zero.

The Attempt at a Solution

I would just measure the effective current using the ammeter for different frequencies and then note at which frequency is the maximum, but I am worried about the given voltmeter - any ideas on where to apply it?

 

[Svein]

I would just measure the effective current using the ammeter for different frequencies and then note at which frequency is the maximum, but I am worried about the given voltmeter - any ideas on where to apply it?

Across the capacitor or the inductance. It will show a maximum at resonance.

 

[gneill]

Across the capacitor or the inductance. It will show a maximum at resonance.

That's not true! At DC the capacitor will behave like an open and ALL the voltage will be dropped there (no current!). At very high frequencies the inductor will look like an open and all the voltage will be dropped there (again no current).

So, what's the third choice?

 

[AndrejN96]

That's not true! At DC the capacitor will behave like an open and ALL the voltage will be dropped there (no current!). At very high frequencies the inductor will look like an open and all the voltage will be dropped there (again no current).

So, what's the third choice?

The voltage of the resistor? And if yes, what with it?

EDIT: Will the voltage across the resistor in a resonant AC RLC circuit be equal to the voltage of the source?

 

[Svein]

That's not true! At DC the capacitor will behave like an open and ALL the voltage will be dropped there (no current!). At very high frequencies the inductor will look like an open and all the voltage will be dropped there (again no current).

I meant using an AC voltmeter, of course. At resonance, the voltages across the inductor and the capacitor will be very large and 180° out of phase.

 

[gneill]

I meant using an AC voltmeter, of course. At resonance, the voltages across the inductor and the capacitor will be very large and 180° out of phase.

An AC voltmeter is assumed given that the problem involves AC voltages.

AndrejN96: Voltages across individual components will vary with frequency and fairly smoothly. It would be worthwhile to pick a hypothetical set of component values and sketch the voltages across the components versus frequency (or "cheat" and get ahold of a simulation software to do it for you! LTSpice is excellent and free). A programmable calculator will do in a pinch to calculate and sketch voltage vs frequency. This assumes that you know how to work with impedance or at least reactance.

As you stated in your problem, you expect the current to be maximized at resonance. What does Ohm's law lead you to expect for the resistor voltage at resonance?

As Svein indicated, voltage phase is of interest. What do you know about the impedances of the L and C with frequency? Is there anything special about them at resonance?

 

[rude man]

I meant using an AC voltmeter, of course. At resonance, the voltages across the inductor and the capacitor will be very large and 180° out of phase.

If (1/R)√(L/C) >1 then you'd be right, the resonant frequency would be where the voltage across either L or C is greater than at any other frequency, from dc to infinity. But if R > √(L/C) this would not be true. So the best place for your voltmeter is the one hinted at in post 3.