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

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SUMMARY

The impedance of a circuit consisting of a 400 Ohm resistor, a 300 Ohm inductor, and an unknown capacitor can be calculated if the capacitive reactance (Xc) is known. The voltage source (Vs) is at a 0-degree angle, indicating that the voltage is in phase with the current. At resonance, the inductive reactance (Xl) equals the capacitive reactance (Xc), leading to a total impedance of 400 Ohms, which is purely resistive. Therefore, knowing either the value of the capacitance or the current is essential for precise calculations.

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  • Familiarity with impedance calculations
  • Ability to interpret phase angles in AC circuits
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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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