Calculate Impedance of 400 Ohm Resistor, 300 Ohm Inductor and 50 V Voltage

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Discussion Overview

The discussion revolves around calculating the impedance of a circuit consisting of a 400 Ohm resistor, a 300 Ohm inductor, and an unspecified capacitor, with a 50 V voltage source applied. The participants explore the necessary parameters for calculating impedance, including the role of capacitive reactance and the phase angle of the voltage.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether it is possible to calculate the impedance without knowing the capacitive reactance (Xc) or the current (I).
  • Another participant emphasizes the need for knowing both the inductive reactance (300 Ohm) and the capacitive reactance (Xc) to find the impedance.
  • A later reply introduces the phase angle of the voltage (Vs) at 0 degrees and discusses its implications for the circuit's behavior, suggesting that for Vs to have a negative angle, the terms Vl - Vc must be zero, leading to the conclusion that Xc must equal Xl (200 Ohm).
  • Another participant notes that the angle of Vs is not diagnostic unless related to the current angle, indicating that knowledge of the current phase angle is necessary for drawing conclusions about total reactance.
  • One participant asserts that if the voltage is at 0 degrees, it implies that the circuit is at resonance, leading to the interpretation that the impedance is simply the resistance (400 Ohm).

Areas of Agreement / Disagreement

Participants express differing views on the implications of the phase angle and the conditions for resonance. While some suggest that the circuit is at resonance when the voltage is at 0 degrees, others emphasize the need for additional information about the current phase angle to make definitive conclusions. No consensus is reached regarding the calculation of impedance without knowing Xc.

Contextual Notes

The discussion highlights the dependence on various parameters, such as the value of the capacitance and the relationship between voltage and current phase angles, which remain unresolved. The implications of resonance and phase relationships are also noted as critical to understanding the circuit's behavior.

greg997
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A 400 Ohm resistor is connected in series with an inductor of reactance 300 Ohm and a capacitor C, and a 50 V voltage is applied to the circuit.

Find impedance.
Is it possible to calculate it? Am I missing something or I would need Xc or I to do that? Thank you for a hint.
 
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greg997 said:
A 400 Ohm resistor is connected in series with an inductor of reactance 300 Ohm and a capacitor C, and a 50 V voltage is applied to the circuit.

Find impedance.
Is it possible to calculate it? Am I missing something or I would need Xc or I to do that? Thank you for a hint.

You would need to know Xc or something else about the behavior of the circuit, such as the current, or whether the circuit was being driven at its natural frequency (resonance).
 
you need to know the value of the capacitance and you need to know the inductive reactance (300Ω )and the capacitative reactance Xc
 
Great thanks. One more question. I forgot to mention the Vs is at 0 degrees angle. Does it change anything?
Becouse Vs=sqrt(Vr^2+(Vl-Vc)^2), so I am thinking that in order to have Vs<0 angle , terms Vl-Vc must be zero. So that means the Xc=Xl= 200 Ohm. Am I right about that? Thank you
 
greg997 said:
Great thanks. One more question. I forgot to mention the Vs is at 0 degrees angle. Does it change anything?
Becouse Vs=sqrt(Vr^2+(Vl-Vc)^2), so I am thinking that in order to have Vs<0 angle , terms Vl-Vc must be zero. So that means the Xc=Xl= 200 Ohm. Am I right about that? Thank you

The angle of Vs is not diagnostic unless it's referred to the current angle. That is, you can draw conclusions about the total reactance of the circuit if you know what phase angle the current has with respect to the voltage.
 
Ok, Thank you. I appreciate your help
 
Usually the current is taken to be the reference direction because V and I are in phase for resistance. I would interpret V is at 0degrees to mean that V is in phase with I.
This means that Xc and Xl are equal and the circuit is at resonance.
It means that the impedance is just the resistance = 400ohms
 
Thank you technician.
 

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