# Lec 18 AC series, resonance ```Series R-L-C AC circuits
Most complex we will consider
∆V = ∆Vgenerator
Fig. 21-8, p.699
Voltage across each element
still obeys Ohm-like law:
∆VR ,max = I max R
∆VL ,max = I max X L =
∆VC ,max = I max X C =
What is the same for all three elements?
But their voltage peaks (maximums) occur
VL and VC are always
VR is always _________ period
shifted from VL and VC
Phase difference between I and V
Impedance Z is reactance of L, R C together
Z= R
2
2
+ (X L − X C )
 X L − XC 

R


φ = tan −1 
∆Vgenerator ,max =
Average power delivered to circuit
Speaker impedance matching
Fig. 21-8, p.699
Where does it go?
4Ω
8Ω
30−60Ω
Pav = I rms ∆Vgenerator ,rms cos φ =
= I rmsVR ,rms = I rms R =
2
VR ,rms 2
R
In an LRC circuit, at a certain frequency
X L = 3Ω, X c = 1Ω, and R = 1Ω. The generator voltage is
∆Vgenerator , rms = 10 volts
LRC resonance
Irms
P1. The maximum voltage put out by the generator is ___
V (see rms vs max definition last time).
__
A. 5
C. 14
E. 28
B. 10
D. 20
Frequency
P2. The maximum current in the circuit is ___ A
A. 2.5
C. 5.5
E. 8.5
B. 4.5
D. 6.5
P3. The average power delivered is ____ W
A. 2
C. 6
E. 10
B. 4
D. 8
Current depends on frequency: biggest possible current
occurs when Z is a minimum!
Or can tune circuit to match a certain frequency!
Variable capacitor
P4. If the frequency is doubled the power
A. increases
B. decreases
C. stays the same
World’s simplest