Parallel circuit with resonant branch

In summary, the conversation is about a parallel circuit with two branches, one with a single capacitor and the other with a resistor, inductor, and capacitor. The first part of the conversation was to find the resonant frequency of the branch with all three components, which was determined to be 2054.7 Hz. The second part was to find the magnitude and phase angle of the current drawn for the entire circuit at this frequency. The impedance of the lone capacitor was found to be 35.2 Ohms. The formula for resonance was discussed and the correct frequency was determined to be around 65 kHz. The approach for finding the capacitor impedance was confirmed to be correct and it was noted that at resonance, the inductor and capacitor
  • #1
SimpleJack
4
0
Here's a question my mate asked me to help out with, but I'm a bit stuck, any help would be good. Apologies for not being able to show the circuit (don't know how) so I'll explain it.

A parallel circuit has a supply of 1 Vrms and has 2 branches. The first branch has a single capacitor of 2.2 microFarads. The second branch has a resistor of 5 Ohms, and inductor of 0.2 milliHenrys and a capacitor of 30 nanoFarads.

The first part was to work out the sesonant frequency of the branch with the 3 components, we both got 2054.7 Hz.

The second part was to find the magnitude the magnitude and the phase angle of the current drawn for the entire of the circuit at the frequency of part a (i.e 2054.7Hz). So we worked out that the impedance of the lone capacitor was 35.2 Ohms.

From this point we are at a bit confused. Are we right up to this point and where do we go from here?

Cheers.
 
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  • #2
How did you get the resonant frequency of the 3 component branch?
The equation for resonance, if I'm not mistaken is 1/sqrt(LC)

So given C = 30nF and L = .2mH, resonant frequency should be 408 krads, or about 65 kHz.

Your approach is correct for the capacitor impedance. Remember that a capacitor is purely reactive.

Resonance implies that the L and C cancels out at that frequency, so on the second branch, you only have the resistor left. So you're left with a simple RC parallel circuit connected to a voltage source.
 
  • #3
I get about 65 kHz as well.

The impedance of the 2.2 uF is about 1.1 Ohms at that frequency.



http://ourworld.compuserve.com/homepages/Bill_Bowden/XLC.htm
 
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  • #4
Am I wrong in thinking the formula for resonance was 1 over 2 x pi x sqrt(LC)
 
  • #5
2pi if you need the freq in Hz.

If you did that, you still should get around 64.974 kHz
 
  • #6
OK sorry, I got the figures wrong. The RLC branch is made of a 5 Ohm resistor, a 30nF capacitor and a 0.2H inductor. My bad,

Can anyone shed any more light on this now...?


Thanks.
 
  • #7
2055 Hz Then.

Impedance of the 2.2uF is 35.2 Ohms at 2055 Hz.



http://ourworld.compuserve.com/homepages/Bill_Bowden/XLC.htm
 
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  • #8
Right got that, so a parallel circuit, the resonant branch impedance is 5 Ohm at angle 0, the lone capacitor branch is 35.2 angle -90 deg.

Thats product/sum = 4.9 at angle -8.1 or 4.9+j0.7.

With a source of 1Vrms, how do you work out the current drawn, what is with the "rms" part?

Cheers, almost there.
 
  • #9
Z = 4.9 - j0.7 Still capacitive.. so minus.


Phase angle is about 8.1 deg. tan-1 0.7/4.9 Xc/R

You have to work out the modulus of the impedance . Sq rt of the sums of the squares of R and Xc and then I = V/Z
 

1. What is a parallel circuit with resonant branch?

A parallel circuit with resonant branch is a type of electrical circuit that contains two or more branches connected in parallel, with one of the branches being a resonant circuit. A resonant circuit is one that contains a capacitor and an inductor, and is able to resonate at a specific frequency.

2. How does a parallel circuit with resonant branch work?

In a parallel circuit with resonant branch, the resonant circuit allows for a specific frequency of current to pass through it while blocking other frequencies. This allows for a high amount of current to flow through the resonant branch, while the other branches carry a lower amount of current. This results in a more efficient distribution of current throughout the circuit.

3. What are the benefits of using a parallel circuit with resonant branch?

One of the main benefits of using a parallel circuit with resonant branch is that it allows for efficient distribution of current, resulting in a more stable and reliable electrical system. It also has the ability to filter out unwanted frequencies, making it useful for specific applications such as in audio equipment.

4. How is a parallel circuit with resonant branch different from a series circuit with resonant branch?

In a series circuit with resonant branch, the resonant element (capacitor and inductor) is connected in series with the rest of the circuit. This means that all of the current must pass through the resonant branch, resulting in a lower overall current in the circuit. In contrast, a parallel circuit with resonant branch allows for the resonant branch to receive a high amount of current while the other branches carry a lower amount.

5. What are some common applications of parallel circuits with resonant branch?

Parallel circuits with resonant branch are commonly used in electrical systems that require efficient distribution of current and/or filtering of specific frequencies. Some examples include audio equipment, power supplies, and radio frequency (RF) circuits. They are also used in parallel resonant circuits, which are used to tune radio receivers and transmitters to specific frequencies.

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