|
M
–
–
–
+
+
+
S
10 V
v
o
(
t
)
v
s
(
t
)
2
Ω
Fig. 14-10.3
7. Find the equivalent inductance between A and B in the two possible parallel connections of two
coupled inductors in Fig. 14-10.4.
M
M
L
1
L
2
B
A
(b)
L
1
L
2
B
A
(a)
Fig. 14-10.4
14.30
Magnetically Coupled Circuits
8. The complex power input into the primary side of a lossless transformer with perfect coupling is
100
+
j100 kVA at 230V rms and 50Hz. The load in the secondary side is seen to consume 90kVA
of reactive power along with active power. (i) Find the complex power consumed by the load and
its power factor. (ii) Find the primary winding self-inductance.
9. (i) What is the turns ratio and coupling coefficient of the transformer in the circuit in Fig. 14-10.5?
(ii) Find the primary and secondary currents and voltage across 10
W
resistor as functions of time
if the source has 110 V rms value and 60 Hz frequency.
1
Ω
10
Ω
2
Ω
+
–
+
–
v
o
(
t
)
1 H
0.5 H
M
4 H
L
2
L
1
Fig. 14-10.5
10. Find all angular frequency values for which the input impedance of the circuit shown in Fig. 14-
10.6 is purely resistive.
1
Ω
1
Ω
0.1 H
0.1 H
0.002 F
0.002 F
k
= 0.3
Fig. 14-10.6
11. Find the power dissipated in the resistors and complex power delivered by the source in the circuit
in Fig. 14-10.7 if the voltage source has 110 V rms value at 60 Hz,
100
Ω
100
Ω
1 H
4 H
k
= 1
+
–
Fig. 14-10.7
12. What is the turns ratio n of the ideal transformer in the circuit in Fig. 14-10.8 if the reactive power
delivered by the source (230 V rms at 50 Hz) is zero?
100
Ω
100
Ω
1 H
1:
n
k
= 1
2.533
µ
F
+
–
Fig. 14-10.8
Problems
14.31
13. What should the value of turns ratio n if maximum power is to be transferred to the 8
W
load in the
circuit in Fig. 14-10.9? If the source has 110 V rms value, what is the amount of power transferred
to 8
W
with this turns ratio?
8
Ω
600
Ω
400
Ω
1:
n
+
–
Fig. 14-10.9
14. The sinusoidal voltage source that is driving a load of impedance 16
-
j10
W
at 1 MHz has source
impedance of 1
+
j1
W
at 1MHz. An ideal transformer is introduced between the source and load
such that the power transferred to load is a maximum. Find the turns ratio of the transformer and
value and nature of additional components needed, if any.
15. A transformer used in a DC power supply has 100 turns in the primary and 25 turns in the secondary.
The primary winding resistance is 0.1
W
and secondary winding resistance is 0.15
W
. The step
response of input current with secondary open is found to have a rise time of 0.22 s. The coupling
coefficient is 0.98. (a) Find the self-inductance of windings and the mutual inductance between
them. (b) Find the input admittance function and voltage transfer function when a resistive load
of 2
W
is connected across the secondary. (c) Prepare the pole-zero plot for the transfer function.
(d) Sketch the frequency response plots for output voltage across the load resistance and estimate
the cut-off frequencies and bandwidth.
16. Obtain the step response of output voltage for the transformer in the Problem 15 with a 2
W
load
in the secondary. What are the flux linkages in coils and total energy stored in the transformer
under step response steady-state condition?
17. The transformer used in the circuit in Fig. 14-10.10 is the same as the one in Problem 15. Switch
was in closed position for a long time prior to t
=
0 and it is opened at t
=
0. (i) Find and plot
i
2
(t), v
o
(t) and v
S
(t) for t
≥
0
+
and (ii) Calculate the energy dissipated in the switch and the 2
W
resistance after at t
=
0.
2
Ω
S
M
i
1
v
S
(
t
)
v
o
(
t
)
t=0
10 V
+
+
+
–
–
–
i
2
Fig. 14-10.10
This page is intentionally left blank.
A
active elements, 1.40–1.41
active power, 7.43–7.44
algebraic sum of voltages, 2.4
amplitude, 6.5–6.6
angular frequency, 6.5–6.6
aperiodic waveforms, 6.4
apparent power, 7.43–7.44
average power, 6.21
averaging filter, 12.39–12.40
LC circuit as, 12.39–12.40
B
balanced loads, 8.29
balanced three-phase circuits, 8.11–8.13
balanced three-phase load circuit, 8.27
band-pass characteristic, 12.31
band-pass output, 12.28–12.31
bandwidth, 2.24
C
capacitor, 3.32–3.35, 3.41–3.45
parallel connection of, 3.44
series connection of, 3.41–3.44
carrier modulated communication systems,
14.14
CCCS. See Current-Controlled Current Source
(CCCS)
characteristic time of variation, 1.37
charge, 1.2
circuit solution, 1.1
circuit theorems, 7.32–7.33
circuit theory, 1.13
coefficient of contribution, 5.4
common mode rejection ratio, 2.24
common-mode gain, 2.24
compensation theorem, 5.19–5.21
complementary function, 10.11
complex amplitudes, 7.13–7.15
complex exponential forcing function,
7.7–7.10
complex exponential signals, 13.4
complex power, 7.49
composition waveform, 6.32
RMS value of, 6.32
conductive decoupling, 14.8
conductive equivalent circuit, 14.8
conductivity, 1.9
convolution theorem, 13.24
coupling coefficient, 14.7
critical response, 12.14
current density, 1.8–1.9
current density vector, 1.9
current intensity, 1.9–1.10
current source excitation, 11.15
Current-Controlled Current Source (CCCS), 4.2
cut-off frequency, 11.15
cycle average value, 9.9
cyclic frequency, 6.5–6.6, 9.24
D
damped natural frequency, 12.16
damping factor, 12.14
DC steady-state, 10.28
degenerative feedback, 2.27
differential amplifier, 2.23, 2.33
differential gain, 2.24
direction of current, 1.9
discrete spectrum, 9.23–9.25
distortion, 2.24
distributed model, 1.37
distributed parameter circuits, 1.36
dot polarity convention, 14.5–14.7
double-tuned amplifier, 14.16–14.19
drift speed, 1.9
drift velocity, 1.8–1.9
dynamic circuit, 7.1, 10.31–10.34
linearity and superposition principle in,
10.31–10.34
Index
I.2
Index
E
electric circuit, 1.1
electric current intensity. See current intensity
electromotive force, 1.6–1.7
electrostatic field intensity, 1.4
electrostatic field intensity vector, 1.4
electrostatic force, 1.2
element relations, 2.2
element variables, 2.2
energy, 1.32
even symmetry, 9.11
excitation functions, 2.14
excitation poles, 13.12
excitation zeros, 13.12
exponential decay, 12.16
exponential Fourier series, 9.7–9.9
exponentially damped sinusoidal shape, 12.8
F
fall time, 10.17–10.18
Faraday’s law, 1.21
final value theorem, 13.25
first form of reciprocity theorem, 5.31
first-order RC circuits, 11.1–11.28
first-order RL circuits, 10.1–10.56
flux expulsion, 14.24–14.26
by a shorted coil, 14.24–14.26
forced response, 9.4, 10.27–10.31
Fortesque’s theorem, 8.24
Fourier series, 6.4, 9.10–9.11
analysis of periodic steady-state using,
9.29
conditions for existence of, 9.10–9.11
properties of, 9.15
Fourier series coefficients, 9.11–9.14
Fourier transforms, 6.4
four-wire system, 8.18
frequency response function, 9.5, 10.47
frequency-shifting theorem, 13.21
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