# Series and parallel R-L-C turned circuits

• Engineering
• agata78
In summary, the problem involves a parallel circuit with an inductor of 0.20 H and a resistor of 60 ohms, connected in parallel with a 20 μF capacitor. The task is to determine the resonant frequency, dynamic resistance, current resonance, and Q-factor at resonance. The formula for resonant frequency is fr = 1/2π√(LC), but for practical circuits with non-zero resistance, it is only an approximation. The value for C is given as 20 μF. Dynamic resistance is the same as dynamic impedance and for part 3, V/I must be solved. The problem is complex and requires a precise calculation for the resonant frequency.

## 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

Have you drawn a schematic?

What do you understand by the resonant frequency?

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?

Agata 78 said:
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.

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

Agata 78 said:

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.

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Agata 78 said:
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.