PHYS 222
Worksheet 25 – Power in AC Circuits
Supplemental Instruction
Iowa State University
Leader:
Course:
Instructor:
Date:
Alek Jerauld
PHYS 222
Dr. Paula Herrera-Siklódy
3/26/12
Useful Equations
I
2
V
Vrms 
2
Vsource  Erms cos(t   )
Pave  IrmsVrms cos 
I rms 
Room mean square for current in an AC Circuit
Room mean square for Voltage in an AC Circuit
Common notation for AC Circuit voltage source.
pf  cos( )
Power in AC Circuit. Remember, power only dissipates in
the resistor.
Power factor. The actual power delivered over the total
possible power. The loss in power delivered is due to the
phase angle.
V2 N 2

V1 N1
Transformer voltage, current, and coil-turns relationship
and V1I1  V2 I 2
Diagrams:
Transformer
Related Problems
1) The voltage across the terminals of an ac power supply varies with time according
to
. The voltage amplitude is V0 = 46.0 V. (Book 31.3)
(a) What is the root-mean-square potential difference Vrms?
V
Vrms 
 32.5 V
2
(b) What is the average potential difference Vave between the two terminals of the power
supply?
Vave  0
2) In a series L-R-C circuit, the components have the following values: L= 20.0 mH, C=
140 nF, and R= 350 Ω. The generator has an rms voltage of 120 V and a frequency of
1.25 kHz. (Book 31.26)
(a) Determine the average power supplied by the generator
E
Erms
I rms  rms 
 0.1446 A
2
Z
X  X   R
L
C
 X L  XC 
  1.135 rad
R


P  I rmsVrms cos    7.32 W
  tan 1 
(b) Determine the average power dissipated in the resistor
PR  P  7.32 W
3) A series ac circuit contains a 270 Ω resistor, a 16.0 mH inductor, a 3.70 μF capacitor,
and an ac power source of voltage amplitude 45.0 V operating at an angular frequency
of 360 rad/s. (Book 31.30)
(a) What is the power factor of this circuit?

 X  XC 
cos   cos  tan 1  L
   0.341
R



(b) Find the average power delivered to the entire circuit.
I
E
E
I rms 


 0.04016 A
2
2 Z 2
 X  X   R2 2
L
C
P  I rmsVrms cos    0.435 W
(c) What is the average power delivered to the resistor, to the capacitor, and to the
inductor?
PR  P  0.435 W
PL  0
PC  0
4) A transformer connected to a 120-V(rms) ac line is to supply 13000 V(rms) for a neon
sign. To reduce shock hazard, a fuse is to be inserted in the primary circuit; the fuse is to
blow when the rms current in the secondary circuit exceeds 8.50 mA. (Book 31.38)
(a) What is the ratio of secondary to primary turns of the transformer?
N 2 V2
  108
N1 V1
(b) What power must be supplied to the transformer when the rms secondary current is
8.50 mA?
V1I1  V2 I 2  P1  V2 I 2  110.5 W
(c) What current rating should the fuse in the primary circuit have?
VI
V1I1  V2 I 2  I1  2 2  0.921 A
V1