# Series and parallel R-L-C turned circuits

• Engineering

## 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?!

## The Attempt at a Solution

NascentOxygen
Staff Emeritus
Have you drawn a schematic?

What do you understand by the resonant frequency?

rude man
Homework Helper
Gold Member
Show some work! You can at least calculate the current for the parallel network.

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
Homework Helper
Gold Member
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.

Last edited:

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

rude man
Homework Helper
Gold Member

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.

Last edited:
NascentOxygen
Staff Emeritus
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.