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

[pat666]

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)
Z_t=√(R²+(X_L-X_C )² )
Z<sub>t[/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.</sub>

 

[rl.bhat]

Current I is along the x-axis.
V_R is along + x-axis

V_L is along +y-axis

VC is along - y-axis.

 

[pat666]

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??

 

[rl.bhat]

Yes. The phasor diagrams are always drawn in that way.

Other things appear to be quit OK.

 

[pat666]

ok Thanks I will make that change