Series and parallel R-L-C turned circuits

[agata78]

Homework Statement

A coil of inductance 0.20 H, resistance 60 ohms is connected in parallel with a 20 μF capacitor across a 20 V, variable frequency supply.
Determine:
1. the resonant frequency
2. the dynamic resistance
3. current resonance
4. Q- factor at resonance

Is anyone there who could help me to go through with this question please?!

Homework Equations

The Attempt at a Solution

 

[NascentOxygen]

Have you drawn a schematic?

What do you understand by the resonant frequency?

 

[rude man]

Show some work! You can at least calculate the current for the parallel network.

 

[agata78]

I believe the resonant frequency equation is:

fr = 1 / 2∏√(LC)

However, I am struggling to work out the value for C (Capacitance). As in the question I have 20uF capacitor.

Is 20uF the value for C?

 

[rude man]

I believe the resonant frequency equation is:

fr = 1 / 2∏√(LC)

However, I am struggling to work out the value for C (Capacitance). As in the question I have 20uF capacitor.

Is 20uF the value for C?

Yes. fr is also correct.

For par 2 I don't know what is meant by 'dynamic resistance'. Is it the real component of impedance or is it ∂V/∂I without regard to phase?

For part 3 you must solve V/I. You will find that the 'current resonance" is not the resonance of part 1.

Part 4 is messy.

In fact, this is a very messy problem altogether except for part 1.

 

[agata78]

Can you please help me work out the value of C for Part 1?

For Part 2. Dynamic resiatance is the same as dynamic impedance.

 

[rude man]

Can you please help me work out the value of C for Part 1?

For Part 2. Dynamic resiatance is the same as dynamic impedance.

You just suggested C = 20 uF and I said "Yes".

So the answer is dynamic resistance = dV/dI? At resonance or anywhere?

I have to warn you, this is a bear of a problem.

 

[NascentOxygen]

I believe the resonant frequency equation is:

fr = 1 / 2∏√(LC)

No, not precisely. That is true for an ideal resonant circuit where R=0. For any practical circuit, with non-zero R, that is only a handy approximation. This problem requires that you determine the precise resonant frequency.

However, I am struggling to work out the value for C (Capacitance). As in the question I have 20uF capacitor.

Is 20uF the value for C?

Yes. The problem specs give you R, L and C. Draw that circuit and write an expression for the impedance of each element, in Ohms.