Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1)
The conversion from the polar form of acomplex number to the rectangular form, or vice–versa,
1)
A)
requires calculus.
B)
is based on trigonometry.
C)
is based on geometry.
D)
must be done using amodern scientific calculator.
2)
“–j” in acomplex number represents
2)
A)
an angle of –90°.
B)
an angle of 0°.
C)
an angle of 90°.
D)
This has no relationship to complex numbers.
3)
Aphasor
3)
A)
hasthe time dependence removed but assumed.
B)
is acomplex number.
C)
represents an AC sinusoidal steady–state signal.
D)
All of the above
4)
The impedance of an inductor
4)
A)
is the phasor voltage–to–current ratio.
B)
shows the AC voltage lagging the current by 90°.
C)
incorporates both the resistance and the phase relationship.
D)
None of the above
5)
For aresistor,
5)
A)
the impedance incorporates phase relationship of +45°.
B)
the impedance incorporates reactance of the resistance.
C)
the impedance incorporates the resistance.
D)
the voltage leads the current by 45°.
6)
Capacitive reactance is
6)
A)
apositive complex number.
B)
the voltage–to–current magnitude ratio for acapacitor.
C)
anegative real number.
D)
the current–to–voltage magnitude ratio for acapacitor.
B
7)
Mathematical operations with AC voltages and currents in the time domain requires
7)
A)
phasors.
B)
manipulation of trigonometry identities.
C)
calculus.
D)
geometry.
B
8)
Impedances for resistances, inductors, and capacitors, and the phasor voltages and currents are
used for
8)
A)
circuit analysis in the time domain.
B)
DC circuit analysis.
C)
AC circuit analysis.
D)
None of the above
C
9)
The subtraction of complex numbers
9)
A)
results in real and imaginary parts.
B)
requires the use of acalculator.
C)
cannot be done using the rectangular form.
D)
requires the addition of corresponding real and imaginary parts.
A
C
10)
The addition of complex numbers
10)
A)
always results in real and imaginary parts.
B)
requires subtraction of corresponding real and imaginary parts.
C)
can be done using the rectangular form.
D)
requires the use of acalculator.
11)
Complex numbers
11)
A)
include magnitude and phase in polar form.
B)
include real and imaginary parts in rectangular form.
C)
contain two pieces of numerical information.
D)
All of the above
12)
For acapacitor,
12)
A)
the impedance incorporates resistance of the capacitor.
B)
capacitive reactance is directly proportional to frequency.
C)
current leads the voltage by 90°.
D)
the impedance incorporates phase relationship of +90°.
13)
AC circuit analysis is performed as it was in DC except
13)
A)
one must use phasors for the voltages and currents.
B)
one must use phasors for the impedance.
C)
complex numbers for the V/I ratio are used to represent the power.
D)
None of the above
14)
Multiplication of complex numbers
14)
A)
is usually done using polar form.
B)
can be done using acalculator.
C)
you multiply the magnitudes and algebraically add the angles.
D)
All of the above
15)
For an inductor,
15)
A)
reactance is the voltage–to–current magnitude ratio.
B)
reactance is inversely proportional to frequency.
C)
inductive reactance is acomplex number.
D)
reactance is anegative real number.
16)
Division of complex numbers
16)
A)
is usually done using polar form.
B)
must be done using acalculator.
C)
you divide the magnitudes and algebraically add the angles.
D)
All of the above
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
17)
Given a(t) = 10sin(377t + 45°) and b(t) = 5sin(377t + 60°),the quotient b(t)/a(t) is ________.
17)
18)
Given that v(t) = 25sin(377t + 45°)V, the RMS value of the voltage is ________.
18)
19)
Given aparallel circuit consisting of a100ohm resistor and a100mH inductor and av(t) =
50sin(1000t + 0°) V source, the RMS phasor current through the inductor is ________.
19)
20)
Given aparallel circuit consisting of a100ohm resistor and a100mH inductor and av(t) =
50sin(1000t + 0°) V source, the RMS phasor voltage across the inductor is ________.
20)
21)
Given v(t) = 50sin(377t + 0°) V and i(t) = 5sin(377t + 90°) mA, the phasor current is
________.
21)
22)
Given aparallel circuit consisting of a100ohm resistor and a100mH inductor and av(t) =
50sin(1000t + 0°) V source, the total circuit impedance is ________.
22)
23)
Given v(t) = 50sin(377t + 0°) V and i(t) = 5sin(377t + 90°) mA, the impedance is ________.
23)
24)
Given aseries circuit consisting of a100 ohm resistor and a10 µF capacitor and av(t) =
50sin(1000t + 0°) V source, the peak phasor voltage across the capacitor is ________.
24)
25)
Given v(t) = 50sin(377t + 0°) V and i(t) = 5sin(377t + 90°) mA, the phasor voltage is
________.
25)
26)
Given aseries circuit consisting of a100 ohm resistor and a10 µF capacitor and av(t) =
50sin(1000t + 0°) V source the total peak phasor current is ________.
26)
27)
Given that v(t) = 25sin(377t + 45°)V, the RMS phasor voltage is ________.
27)
28)
Express the complex numbers 2500/+30.0°in rectangular form ________.
28)
29)
Express the complex numbers 1000 + j2000 in polar form ________.
29)
30)
Given that v(t) = 25sin(377t + 45°)V, the peak voltage is ________.
30)
5
31)
Given aseries circuit consisting of a100 ohm resistor and a10 µF capacitor and av(t) =
50sin(1000t + 0°) V source, the RMS phasor voltage across the resistor is ________.
31)
32)
Given aseries circuit consisting of a100 ohm resistor and a10 µF capacitor and av(t) =
50sin(1000t + 0°) V source, the current as afunction of time is ________.
32)
33)
Given aparallel circuit consisting of a100ohm resistor and a100mH inductor and av(t) =
50sin(1000t + 0°) V source, the total peak phasor current is ________.
33)
34)
Given aseries circuit consisting of a100 ohm resistor and a10 µF capacitor and av(t) =
50sin(1000t + 0°) V source, the total impedance of the circuit is ________.
34)
35)
Given aparallel circuit consisting of a100ohm resistor and a100mH inductor and av(t) =
50sin(1000t + 0°) V source, the peak phasor current through the resistor is ________.
35)
TRUE/FALSE. Write ‘T’ if the statement is true and ‘F’ if the statement is false.
36)
The conversion from the polar form of acomplex number to the rectangular form, or vice–versa, is
based on trigonometry.
36)
37)
Modern scientific calculators perform conversions between polar and rectangular form
automatically.
37)
38)
If you do the AC circuit analysis in the time domain, (i.e., using the sinusoidal functions) it
CANNOT be performed as it was when you did DC circuit analysis.
38)
39)
AC circuit analysis can be performed as it was in DC except one must use phasors for the voltages
and currents and complex numbers for the V/I ratio (impedance) for R, L, and C.
39)
40)
When you multiply complex numbers with amodern calculator, you can ONLY use polar form.
40)
41)
The “j” in acomplex number is equivalent to the angle of 90°.
41)
42)
When you perform addition or subtraction with complex numbers you can add or subtract the
corresponding real and imaginary parts of the complex numbers to determine the result.
42)
43)
The AC voltage lags the current by 90°for an inductor.
43)
44)
When you perform division with complex numbers you can use polar form.
44)
45)
The impedance of acapacitor incorporates both the reactance and the phase relationship of the
phasor voltage–to–current ratio for the capacitor.
45)
46)
The two pieces of information needed to represent complex numbers in rectangular are the real and
imaginary parts.
46)
47)
Capacitive reactance is directly proportional to frequency and capacitance.
47)
48)
The AC current lags the voltage by 90°for acapacitor.
48)
49)
Complex numbers make mathematical operations with AC voltages and currents more
cumbersome than they would be in the time domain.
49)
50)
Inductive reactance, XL,is areal, positive number that is the voltage–to–current magnitude ratio for
an inductor.
50)
51)
The impedance of aresistance incorporates both the resistance and the phase relationship of the
phasor voltage–to–current ratio for the resistance.
51)
52)
The AC current lags the voltage by 90°for aresistor.
52)
53)
Inductive reactance is inversely proportional to frequency and inductance.
53)
54)
When multiplying complex numbers you multiply the angles and algebraically add the
magnitudes.
54)
55)
Aphasor is acomplex number representation of an AC sinusoidal steady–state signal with the
sinusoidal time dependence removed but assumed.
55)
56)
When you divide complex numbers you divide the magnitude of the numerator by the magnitude
of the denominator and algebraically subtract the angle of the denominator from the angle of the
numerator.
56)
57)
Impedances are used for resistances, inductors, and capacitors, and phasors are used for voltages
and currents in AC circuit analysis.
57)
58)
The impedance of an inductor incorporates both the reactance and the phase relationship of the
phasor voltage–to–current ratio for the inductor.
58)
59)
Capacitive reactance, XC,is areal, positive number that is the voltage–to–current magnitude ratio
for acapacitor.
59)
60)
You must use the rectangular form of acomplex number to perform addition or subtraction with
complex numbers when using amodern calculator.
60)
61)
Magnitude and phase are the two pieces of information needed to represent complex numbers in
polar form.
61)
Answer Key
Testname: C8
Answer Key
Testname: C8
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