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

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.

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

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

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

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

Equivalent Circuits for Magnetically Coupled Coils

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

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

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

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

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,

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. Use the T-equivalent circuit.

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.

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?

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