Circuit analyse -- LR circuit frequency response

In summary, the conversation discusses the techniques and equations needed to solve for X in the given circuit problem involving a resistor and an inductor. The individual has attempted various methods but has not been successful in finding a solution. They mention using phasors and the transfer function, and the possibility of using the voltage divider. The conversation also touches upon the use of phasor impedances and provides a suggestion to search for examples on Google to better understand the concept.
  • #1
8700
25
1

Homework Statement



Find X [/B]

upload_2016-11-14_19-41-44.png

Homework Equations



V1(t)=8cos(12000t)
V0(t)=Xcos(12000t+θ)

The Attempt at a Solution


[/B]
I've tried quiet a lot actually, but all in vain. Seems like I am either misunderstanding something, or i am just too tired to think at the moment. Either way, I am frustated!
 
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  • #2
8700 said:

Homework Statement



Find X [/B]

View attachment 108908

Homework Equations



V1(t)=8cos(12000t)
V0(t)=Xcos(12000t+θ)

The Attempt at a Solution


[/B]
I've tried quiet a lot actually, but all in vain. Seems like I am either misunderstanding something, or i am just too tired to think at the moment. Either way, I am frustated!
What technique would you expect to use for this type of problem? If the inductor were replaced with a resistor, what would your answer be?

Have you worked with Phasors? What about Differential Equations? You will probably use one of those techniques to solve this, depending on what you have been learning in class...
 
  • #3
we have mostly been working with phasors, which is those tools i am using.

I know that the following.

v(t)=Re{Vejωt}=VAcos(ωt+Φ)

and

V=VAe=VA∠Φ

somehow I can't seem to get further then this.

I am considering to use the transfer function, and use that to solve for X
 
Last edited:
  • #4
8700 said:
we have mostly been working with phasors, which is those tools i am using.

I know that the following.

v(t)=Re{Vejωt}=VAcos(ωt+Φ)

and

V=VAe=VA∠Φ

somehow I can't seem to get further then this.

I am considering to use the transfer function, and use that to solve for X
If the inductor were replaced with a resistor, what technique would you use?

And with the inductor put back in place, how can you use phasor impedances to do a similar calculation?
 
  • #5
Hmm I would probably use the voltage divider

Could I not do that with the transfor function?
 
  • #6
8700 said:
Hmm I would probably use the voltage divider

Could I not do that with the transfor function?
:smile:
 
  • #7
I take that as an yes :D
 
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Likes berkeman
  • #8
8700 said:
I take that as an yes :D
Yep. And if you want to see some good examples of how to work with them, just do a Google Images search on Phasor Voltage Divider... :smile:
 

1. What is a LR circuit?

A LR circuit is a type of electronic circuit that contains a combination of inductors (L) and resistors (R). It is used to control the flow of electrical current and is commonly used in filter circuits, oscillators, and amplifiers.

2. How does a LR circuit respond to different frequencies?

The response of a LR circuit to different frequencies can be analyzed by looking at its frequency response. This refers to how the circuit's output voltage changes in response to different input frequencies. The frequency response of a LR circuit is affected by the values of the inductance and resistance, as well as the frequency of the input signal.

3. What is the resonant frequency of a LR circuit?

The resonant frequency of a LR circuit is the frequency at which the circuit will have the highest response or the greatest amplitude. This occurs when the inductive reactance (XL) and the resistive reactance (XR) are equal, resulting in a purely resistive circuit. The resonant frequency can be calculated using the formula f = 1/2π√(LC), where L is the inductance and C is the capacitance of the circuit.

4. How do you calculate the impedance of a LR circuit?

The impedance of a LR circuit can be calculated using the formula Z = √(R^2 + (XL - XR)^2), where R is the resistance, XL is the inductive reactance, and XR is the resistive reactance. The impedance is a measure of the total opposition to current flow in the circuit and is affected by the values of the inductance, resistance, and frequency.

5. What is the phase relationship between voltage and current in a LR circuit?

In a LR circuit, the voltage and current are out of phase, meaning they do not peak at the same time. The voltage in a LR circuit lags behind the current by 90 degrees. This is due to the inductor's property of opposing changes in current, resulting in a delay in the voltage across the inductor.

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