Download PHYS 222 Worksheet 24 More AC Circuits

PHYS 222
Worksheet 24 – More 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
3/22/12
Related Problems
1) You have a 200 ohm resistor, a 0.400-H inductor. Suppose you take the resistor and
inductor and make a series circuit with a voltage source that has voltage amplitude 30.0 V
and an angular frequency of 250 rad/s. For this R-L circuit graph V, VR, and VL
versus t for t = 0 to t = 50.0 ms. The current is given by I = I cos(wt) so v = V cos(ωt + φ).
(Draw the phasor diagram)
E
E
I 
 0.1342 A
2
2
Z
 L   R
VL  IX L  13.42 V
VR  30 V
2) You have a 200-Ω resistor, a 0.400-H inductor, a 6.00-μF capacitor and a voltage source
that has a voltage amplitude of 30.0 V and an angular frequency of 250 rad/s. The resistor,
inductor, capacitor, and voltage source are connected to form an L-R-C series circuit. The
current is given by I = I cos(ωt), so v = V cos(ωt + φ). Graph v, VR, VL, and VC as a function
of time for t = 0 to t = 27 ms.
(Draw the phasor diagram)
E
E

 0.05 A
2
Z
1 

2
 L 
 R
C 

VL  IX L  5 V
I
VR  30 V
VC  IX C  33.3 V
3) An ac source whose rms voltage is 80 V is in series with a 100- ohm resistor and a
capacitor, whose reactance is 200 ohms at the frequency of the source. The instantaneous
current, when the voltage of the source is zero and is increasing, is closest to:
(a) zero
(b) 0.23 A
(c) 0.16 A
(d) 0.45 A
(d) 0.32 A
 200 
  1.107 rad
 100 
v  0  RI cos t     cos t     0
  tan 1 
t    cos 1 (0)   / 2  t 
i  I max cos(t ) 
2.678

rad
E
80 2
 2.678 
cos t  
cos  
 0.4525 A
Z
 

2002  1002
4) An R-L-C series circuit is constructed using a 175-ohm resistor, a 12.5-µF capacitor, and
an 8.00-mH inductor, all connected across an ac source having a variable frequency and a
voltage amplitude of 25.0 V.
(a) At what angular frequency will the impedance be smallest?
Z min  X L  X C  0
 X L  X C  L 
1
C
1
 3160 rad / s
LC
(b) What is the impedance at this frequency?
 
Z min 
 X L  XC 
2
 R 2  R  175 
(c) At the angular frequency in part A, what is the maximum current through the inductor?
E 25
I 
 0.143 A
Z 175
(d) At the angular frequency in part A, find the potential difference across the ac source, the
resistor, the capacitor, and the inductor at the instant that the current is equal to one-half its
greatest positive value.
i  I max cos t 
0.143
 0.143cos  3160t 
2
 t  0.000331

vL  IX L cos t   / 2   3.13 V
vC  IX C cos t   / 2   3.13 V
vR  IR cos t   12.5 V
v  E cos t   12.5 V