1. 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 V, and it is operating at 800 rad/s. The transformer parameters are R1 = 100Ω, L1 = 0.5 H, R2 = 40Ω, L2 = 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.

2. Ideal Transformer

3. Example
4:1
ideal
60Ω
40Ω
20Ω
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.

4. +
4:1 -
60Ω V1 V2 -
ideal + +
40Ω - i1 i2
20Ω
Solution
a).

5. The solutions for V1, V2, I1 and I2 are
The voltage across the 5 A current source is

6. The average power associated with the current source is
b).
To find the average power delivered to the 20Ω resistor

7. Drill Exercise
Find the average power delivered to the 4 kΩ resistor in circuit shown.
ideal
1:2.5
1:4
10Ω
4kΩ

8. Equivalent Circuits for Magnetically Coupled Coils

9. Rangkaian Ekivalen model T
L1-M
L2-M a R2 c + + i1 i2 M v2 v1 - - b d

10. Rangkaian Ekivalen model c + i1 + i2 v2 v1 - - b d

11. Example + + V1 V2 - - a. 6H 1H 3H

12. 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.
At an operating frequency of 400 rad/s,
j2400
j400
j1200

14. b).
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.
j4800
j2800
-j1200
At an operating frequency of 400 rad/s,

17. 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 V, and it is operating at 800 rad/s. The transformer parameters are R1 = 100Ω, L1 = 0.5 H, R2 = 40Ω, L2 = 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.

18. a). The rms magnitude of V0
256∠0o V (rms)
15Ω
j50Ω
j20Ω
j32Ω
80Ω V0 + -
Calculate :
a). The rms magnitude of V0
b). The average power dissipated in the 80 Ω resistor.

19. What is the maximum average power delivered to 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?

20. 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