PHYS 222 Worksheet 23 AC Circuits ANSWERS

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PHYS 222
Worksheet 23 – AC Circuits
Supplemental Instruction
Iowa State University
Useful Equations
RLC Circuit:
Phasors: ALWAYS draw the diagram!!
Z  ( X L  X C )2  R 2
E  (VL VC )2  VR 2
E  IZ
tan  
X L  XC
R
Leader:
Course:
Instructor:
Date:
Alek Jerauld
PHYS 222
Dr. Paula Herrera-Siklódy
3/20/12
Related Problems
1) A capacitance C = 3.60 μF and an inductance L = 5.10 mH are operated at the same
angular frequency. What is the reactance of each element? (Book 31.6)
1

LC
X L  L 
XC 
1
L
L
 37.6 
C
LC
1

C
1
L

 37.6 
1
C
C
LC
2) A 150-ohm resistor is connected in series with a 0.250-H inductor. The voltage across
the resistor is: (Book 31.13)
(a) Which of the following is the correct equation for the current in this circuit?:
a)
b)
c)
d)
I
E
Z
Z  R 2  ( X L  X C ) 2  R 2  X L 2  R 2   L 
I 
E
R 2   L 
2
2
 0.0253 A
 i  0.0253cos  720t 
(b) Determine the inductive reactance of the inductor.
X L   L  180 
3) You have a 210-ohm resistor and a 0.410-H inductor. Suppose you take the resistor and
inductor and make a series circuit with a voltage source that has a voltage amplitude
of 31.0 V and an angular frequency of 260 rad/s. (Book 31.14)
(a) What is the impedance of the circuit?
Z  R 2   X L  X C   R 2   L   236 
2
(b) what is the current amplitude?
E
I   0.132 A
Z
2
(c) What is the voltage amplitude across the resistor?
VR  IR  27.6 V
(d) What is the voltage amplitudes across the inductor?
VL  IX L  14.0 V
(e) Does the source voltage lag or lead the current?
X 
  tan 1  L   26.9
 R 
Phase angle is positive, so voltage source is LEADING the current.
(f) Draw the phasor diagram
4) You have a 201 -ohm resistor, a 0.401 H inductor, a 5.00 -μF capacitor, and a variablefrequency ac source with an amplitude of 3.01 V. You connect all four elements together to
form a series circuit. (Book 31.21)
(a) At what frequency will the current in the circuit be greatest?
Current is greatest when Z is smallest. Z is smallest when Z = R or XL = XC:
Z  R  X L  XC
 L 
1
 
C
1
 706 rad / s
LC
(b) What will be the current amplitude at this frequency?
E
Z  R  I   0.015 A
R
(c) What will be the current amplitude at an angular frequency of 401 rad/s?
E
E
I 
 0.00765 A
Z
1 

2
R  L 
C 

(d) At this frequency, will the source voltage lead or lag the current?
1 

  L  C 
1
  tan 
  59 Phase angle is negative, so Voltage source is Lagging Current
R




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