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Drill Exercise A linear transformer couples a load consisting of a 360 Ω resistor in series with a...
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Transcript of Drill Exercise A linear transformer couples a load consisting of a 360 Ω resistor in series with a...
Drill Exercise
A linear transformer couples a load consisting of a 360 Ω resistor in series with a 0.25 H inductor to a sinusoidal voltage source, as shown. The voltage source has an internal impedance of 184+j0 Ω and a maximum voltage of 245.20 V, and it is operating at 800 rad/s. The transformer parameters are R1 = 100Ω, L1 = 0.5 H, R2 = 40Ω, L2 = 0.125 H, and k = 0.4. Calculate :
a). The reflected impedance,
b). The primary current, c). The secondary current, and
d). The average power delivered to the primary terminals of the transformer.
Ideal Transformer
rms
A005
60Ω
4:1
40Ω
20Ω
ideal
Example
a). Find the average power delivered by the sinusoidal current source in the circuit shown.
b). Find the average power delivered to the 20 Ω resistor.
+
-
i1i2
4:160Ω
rms
V0030040Ω
20Ω
V1 V2
+
+ -
- ideal
Solution
2212
2111
40200
2060300
IVII
IIVI
a).
12141
2 4I IVV
The solutions for V1, V2, I1 and I2 are
rmsAI
rmsAI
rmsVV
rmsVV
0.1
25.0
65
260
2
1
2
1
The voltage across the 5 A current source is
rmsV
IIVV A
285125.020260
20 2115
The average power associated with the current source is
WP 14255285 b). To find the average power delivered to the 20Ω resistor
WP
rmsAIII
25.312025.1
25.1125.02
20
2120
Find the average power delivered to the 4 kΩ resistor in circuit shown.
idealideal
1:2.5 1:4
rms
V00100
10Ω
4kΩ
Drill Exercise
dt
diL
dt
diMv
dt
diM
dt
diLv
22
12
2111
Equivalent Circuits for Magnetically Coupled Coils
Rangkaian Ekivalen model T
L1-M L2-M R2R1
M
a c
b d
v1v2
+ +
- -
i1 i2
Rangkaian Ekivalen model
M
MLL 221
ML
MLL
2
221
ML
MLL
1
221
R1 R2a c
b d
v1v2
+ +
- -
i1 i2
+
-
+
-
V1 V2
V00300
3600j
500 100j 200 800100
2500j
1200j
1I2I
1600j
a.
Example
3H
6H 1H
j2400 j400
j1200
HM
HML
HML
3
134
639
2
1
At an operating frequency of 400 rad/s,
For the polarity dots shown in this example, M carries a value of +3 H in the T equivalent circuit.
0210090012002500700
300
j
V
j
V
j
V
VjV o37,324,1368136
b).
rmsmAj
jI o57,7125,63
2500700
81363001
rmsmAj
jI o43,6363,59
2100900
81362
j4800 j2800
-j1200
HM
HML
HML
3
734
1239
2
1
At an operating frequency of 400 rad/s,
When the polarity dot is moved to the lower terminal of the secondary coil, M carries a value of -3 H in the T equivalent circuit.
rmsmAI o57,7125,631
rmsmAI o57,11663,592
030090012004900700
300
j
V
j
V
j
V
rmsmAj
jI
rmsmAj
jI
rmsVjV
02
1
0
57.11663.59300900
568
57.7125.634900700
568300
13.9857.56568
A linear transformer couples a load consisting of a 360 Ω resistor in series with a 0.25 H inductor to a sinusoidal voltage source, as shown. The voltage source has an internal impedance of 184+j0 Ω and a maximum voltage of 245.20 V, and it is operating at 800 rad/s. The transformer parameters are R1 = 100Ω, L1 = 0.5 H, R2 = 40Ω, L2 = 0.125 H, and k = 0.4. Calculate : a). The reflected impedance, b). The primary current, c). The secondary current, and d). The average power delivered to the primary terminals of the transformer.Use the T-equivalent circuit.
Drill Exercise
256∠0o V (rms)
15Ω j50Ω
j20Ωj32Ω
80Ω
V0
+
-
Calculate :a). The rms magnitude of V0
b). The average power dissipated in the 80 Ω resistor.
+
-ZL
480∠0o
V (rms)
20Ω
j35Ω 40Ω
j50Ω 15Ω
j45Ω
j80Ω
The impedance ZL in the circuit shown is adjusted for maximum average power transfer to ZL. The internal impedance of the sinusoidal voltage source is 20+j35 Ω.
What is the maximum average power delivered to ZL?
200Ω
15mH
20mH 25mH
88Ω
vg
Find the average power delivered to the 200 Ω resistor in the circuit shown if
vg= 424 cos 8000t V