ENG17, Sec. 2 (Montgomery)
Spring 2014
1. (5 points) For parts (a)-(e) below, write the equivalent unit from the bank of options given here:
OPTIONS: [C/V], [J/s], [A∙s], [J/C], [V/A], [s/rad], [C/s], [A/V], [V∙s], [Wb/A], [rad/s], [1/s]
Given
Equivalent
Value
(a)
Watt [W]
1 pt
(b)
Farad [F]
1 pt
(c)
Weber [Wb]
1 pt
(d)
Henry [H]
1 pt
(e)
Coulomb [C]
1 pt
2. (10 points, 1 pt each) For parts (a)-(j) below, fill in the blank:
OPTIONS: [voltage, capacitance, reflected, ideal transformer, reactive, power factor, reactive power,
current, maximum power, apparent power, average power, impedance, resistance, time constant,
transmitted, real, admittance, linear transformer, reactive factor, magnetic, inductance]
(a) ______________________________ is the energy per unit charge created by charge separation.
(b) ______________________________ is the rate of charge flow.
(c) ______________________________ is the linear circuit parameter that relates the voltage induced by a
time-varying magnetic field to the current producing the field.
(d) ______________________________ is the linear circuit parameter that relates the current induced by a
time-varying electric field to the voltage producing the field.
(e) ______________________________ of an RL circuit equals the equivalent capacitance times the
Thevenin resistance as viewed from the terminals of the equivalent capacitor.
(f) ______________________________ impedance of the secondary circuit as seen from the terminals of
the primary circuit in a transformer.
(g) An ____________________________ is a transformer with the following special properties: perfect
coupling, infinite self-inductance in each coil, and lossless coils.
(h) ______________________________ is the reciprocal of impedance.
(i) ________________________ is the electric power exchanged between the magnetic field of an inductor
and the source that drives it OR between the electric field of a capacitor and the source that drives it.
(j) _______________________ is the cosine of the phase angle between the sinusoidal voltage and current.
3 of 10
ENG17, Sec. 2 (Montgomery)
Spring 2014
3. (10 points) Find V1 and V2 in the circuit below when ω is 1000 rad/s. Express answer in
rectangular form. (recall that 1/j = -j). Simplify answer as much as reasonably possible.
4∠90° V
V2
V1
39 Ω
2 mF
4 mH
4Ω
2∠0° A
Answer
Value
(a)
V1 =
5 pt
(e)
V2 =
5 pt
4 of 10
ENG17, Sec. 2 (Montgomery)
Spring 2014
4. (13 points) Find the Thevenin equivalent of the circuit below, as seen from the
terminals a-b. Also find the impedance of a variable load placed across a-b that would result
in maximum power transfer to that load (part (c)). Express answer in rectangular form.
j2 Ω
2Ω
a
Io
4∠0° A
-j4 Ω
3Io
4Ω
b
Answer
Value
(a)
VTH =
5 pt
(b)
ZTH =
5 pt
(c)
ZL =
3 pt
5 of 10
ENG17, Sec. 2 (Montgomery)
Spring 2014
5. (12 points) Consider a two-terminal element as shown at right. Given
that V = 12∠15° V (the amplitude is peak, not rms) and Z = 2∠-45° Ω,
determine the quantities listed below. You should evaluate the sin/cos
functions. (hint…cos 45°=√2 / 2)
I
+
V
Answer
(a)
(b)
(c)
(d)
(e)
I=
Average Power
P=
Reactive Power
Q=
Apparent Power
A=
Power Factor
pf =
Value
Z
-
2 pt
2 pt
2 pt
2 pt
2 pt
Is the Power Factor
(f)
LAGGING or LEADING? (circle
answer)
2 pt
6 of 10
ENG17, Sec. 2 (Montgomery)
Spring 2014
6. (10 points) In the circuit below, Z1 = 2∠-25° Ω and Z2 = 3∠-25° Ω. Calculate the total (a)
complex power, (b) average (real) power, (c) reactive power, and (d) power factor angle,
supplied by the source and seen by the source. Also, indicate if the power factor is lagging or
leading (part (e)). Note that the source voltage is the RMS value.
Is
Z2
Z1
Answer
(a)
(b)
(c)
(e)
(f)
Complex Power
S=
Average Power
P=
Reactive Power
Q=
Power Factor Angle
θ=
Is the Power Factor
LAGGING or LEADING? (circle answer)
I2
I1
6∠10° V rms
Value
2 pt
2 pt
2 pt
2 pt
2 pt
7 of 10
ENG17, Sec. 2 (Montgomery)
Spring 2014
7. (12 points) For the ideal transformer circuit below, find the phasor voltages and currents
indicated on the schematic. Leave answers in rectangular form. Simplify as much as possible.
The amplitude of the voltage source is peak, not rms).
I1
100 Ω
-j4 Ω
j200 Ω
10:1
100∠0° V
+
+
V1
V2
-
-
4Ω
I2
Answer
Value
(a)
I1 =
3 pt
(b)
I2 =
3 pt
(c)
V1 =
3 pt
(e)
V2 =
3 pt
8 of 10
ENG17, Sec. 2 (Montgomery)
Spring 2014
8. (10 points) The op amp in the circuit below is ideal.
a.
b.
c.
d.
e.
What circuit configuration is shown in the circuit below?
Write an expression for vo in terms of vs.
Write an expression for io in terms of vo.
What are the limits of vs if the op amp operates within its linear region?
What is vo when vs = 4 V?
+15V
+
−
io
-15V
36 kΩ
18 kΩ
18 kΩ
36 kΩ
+
vo
−
vs
Answer
(a)
Value
2 pt
(b)
vo =
2 pt
(c)
io =
2 pt
≤ vs ≤
(d)
(e)
vo =
2 pt
2 pt
9 of 10
ENG17, Sec. 2 (Montgomery)
Spring 2014
9. (18 points) The switch in the circuit below is in position (a) for a long time. At t = 0, the switch
changes to position (b). Determine the values indicated in the answer box below.
4Ω
b
a
t=0
iL
10 V
12 Ω
2H
+
v
2F
−
Answer
Value
(a)
v(0-) =
4 pt
(b)
v(0+) =
2 pt
(b)
iL(0+) =
2 pt
(d)
dv(0+)/dt =
2 pt
(e)
α=
2 pt
(f)
ω0 =
2 pt
(g)
(h)
Damping Condition:
v(α) = Vf =
4Ω
2 pt
2 pt
10 of 10