Determine resonant frequency of an AC voltage source

In summary, the conversation is about finding the resonant frequency of a series RLC circuit experimentally using an AC voltage source, an ammeter, and a voltmeter. The current in the circuit is expected to be maximum at resonance, and the imaginary part of the total impedance/admittance of the circuit is zero. The suggested method is to measure the effective current using the ammeter for different frequencies and note the frequency at which it is maximum. The voltmeter can be used to measure the voltage across the capacitor or the inductor, which will show a maximum at resonance. However, at DC, the capacitor will behave like an open circuit and at very high frequencies, the inductor will behave like an open circuit, so
  • #1
AndrejN96
26
0

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?
 
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  • #2
AndrejN96 said:
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.
 
  • #3
Svein said:
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? :smile:
 
  • #4
gneill said:
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? :smile:
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?
 
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  • #5
gneill said:
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.
 
  • #6
Svein said:
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?
 
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  • #7
Svein said:
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.
 

1. What is a resonant frequency?

A resonant frequency is the specific frequency at which an AC circuit or system naturally oscillates or vibrates with the greatest amplitude. It is determined by the capacitance and inductance of the system.

2. Why is it important to determine the resonant frequency of an AC voltage source?

Determining the resonant frequency allows us to design and operate circuits and systems at their most efficient point. It also helps us avoid unwanted oscillations or resonances that can cause damage to the system.

3. How do you calculate the resonant frequency of an AC voltage source?

The resonant frequency can be calculated using the equation f = 1/ (2π√LC), where f is the resonant frequency, L is the inductance, and C is the capacitance of the circuit or system.

4. What factors can affect the resonant frequency of an AC voltage source?

The resonant frequency can be affected by the inductance and capacitance of the circuit or system, as well as external factors such as temperature and humidity. Altering these factors can change the resonant frequency of the system.

5. How can the resonant frequency of an AC voltage source be measured?

The resonant frequency can be measured using specialized equipment such as an oscilloscope or frequency meter. Alternatively, it can be calculated using the circuit's components and the resonant frequency equation.

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