RLC circuit - total impedance,phasor analysis (mainly checks)

In summary: V. The frequency at which maximum current will flow is 205.5 Hz. The quality factor, Q, of the circuit is 2.58.
  • #1
pat666
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Homework Statement


A resistor, R = 100 Ω, an inductor, L = 0.20 H and a capacitor, C = 3 µF are connected in series across an ac source of VS = 100 V and frequency, f = 200 Hz. Calculate the following for this series circuit:
in attempt at solution


Homework Equations





The Attempt at a Solution



the total circuit impedance (Zt)
Zt=√(R2+(XL-XC )2 )
Zt[/SUB=100.97 ohms , this part I'm pretty confident about - just subbing numbers

the total circuit current (IS)
Irms=Vrms/Z
my rms current should be right but should I include the max current here (needed in nxt Q)?

the voltage drop across each component (VR, VL and VC)
V_R=I_max R V_R=140.1V
V_L=I_max X_L V_L=352.0V
V_C=I_max*X_C V_C=371.5V
These should be right i think

d) the phase angle between VS and It.
tanϕ=(X_L-X_c)/R
ϕ=-8 degrees
will the equation tanϕ=(X_L-X_c)/R give me the phase angle between VS and It or some other angle?


e) Draw the phasor diagram of voltages and current for the circuit.
This one I'm not sure about, Its pretty much exactly the same as the one in my text but vc max should be the vector sum of v rmax and vmax but it is always shorter than those two in the text ands its longer for me? btw its the attached pic

f) What is the frequency of the ac source for maximum current to flow?
I did the resonant frequency for this which i think is right but not totally sure on??
ω_0=√(1/LC)
f=205.5Hz


g) What is the quality factor, Q, of the circuit at the frequency calculated in part f)?
Q=ωL/R
=2.58
This should be right but what are the units for Q factor or is it dimensionless?
thanks for any help.
 

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  • #2
Current I is along the x-axis.
V_R is along + x-axis

V_L is along +y-axis

VC is along - y-axis.
 
  • #3
Thanks,
Is that how phasor diagrams always go, won't they always be the same regardless of the circuit??
anything else that you notice that could be wrong with my answers??
 
  • #4
Yes. The phasor diagrams are always drawn in that way.

Other things appear to be quit OK.
 
Last edited:
  • #5
ok Thanks I will make that change
 

1. What is an RLC circuit?

An RLC circuit is an electrical circuit that contains a resistor (R), inductor (L), and capacitor (C). These components are connected in series or parallel, and their behavior is governed by the principles of Ohm's law and the laws of electricity and magnetism.

2. What is total impedance in an RLC circuit?

Total impedance in an RLC circuit is the total opposition to the flow of current in the circuit. It is a combination of the resistance, inductance, and capacitance of the circuit, and is represented by the symbol Z. Total impedance is calculated using the formula Z = √(R^2 + (XL - XC)^2), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.

3. How is phasor analysis used in RLC circuits?

Phasor analysis is a method used to analyze the behavior of an RLC circuit at a specific frequency. It involves representing the voltage and current in the circuit as phasors (vectors) that rotate at a constant angular frequency. By using phasor diagrams and complex numbers, we can determine the amplitude and phase relationships between voltage and current in the circuit.

4. What are some important checks to perform in RLC circuit analysis?

When analyzing an RLC circuit, it is important to check for several things. One check is to ensure that the total impedance is greater than the resistance alone, as this indicates the presence of inductive and/or capacitive elements. Another important check is to make sure the phase angles of the impedance components are correct in relation to the total impedance. Additionally, checking the power factor and resonance frequency can provide valuable insights into the behavior of the circuit.

5. How is an RLC circuit used in real-world applications?

RLC circuits are widely used in various electronic devices and systems. They can be found in power supplies, filters, oscillators, and many other applications. In power supplies, RLC circuits are used to regulate voltage and current flow. In filters, they are used to separate or combine specific frequencies. In oscillators, they are used to generate and control oscillations. Overall, RLC circuits are essential components in many electrical and electronic systems.

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