Review of AC-circuit
Keys to deal with R, L, and C in an AC-circuit
•
•
•
Across R, voltage and current are in-phase
Across L, the current lags behind voltage by 90o
Across C, the current leads voltage by 90o
Also,
•
•
When two elements are in series  the same current
passing through them
When two elements are in parallel  the same voltage
across them
Basics
R
L
I and V are in-phase
I lags V by 90 degree
I leads V by 90 degree
C
RLC in series
Key: IR, IL, and IC are all in phase
DVR ~ R
DVL ~ XL
DVC ~ XC
DVmax ~ Z
Z 
  tan
R  (X L  XC )
2
1
 XL  XC 


R


2
What if RLC are not in series?
Which of the following is true
(a) DVc = DVL, IC = IL
(b) DVc = DVL, IR = IL
(c) DVc = DVR, IR = IL
(d) DVL = DVR, IR = IL
(e) DVc = DVL+ DVR, IC = IL
(f) DVc = DVL+ DVR, IR = IL
DVL
How do you draw the phasor diagram?
Imax
DVc = DVR+ DVL
IC
IR = IL
DVR
Power dissipation
• Only R dissipates power
P = I *DV, always
For L and C, I and DV are 90o out of phase  PL = 0, PC = 0
For R, I and DV are in-phase  PR = IDV = Irms2R
Resonance in RLC circuit in series
Z 
R  (X L  XC )
2
 XL  XC 
  tan 

R


1
PR = IDV = Irms2R
Where Irms = Vrms/Z
For a fixed AC voltage source,
maximum power dissipation occurs
when XL = XC, ie. When Z = R
i.e.  
1
LC
2