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