1. Determine *I**X*, assuming *I**SRC*= 1 A (Hint: write one KVL equation and one KCL equation).

A. 4 A

B. 2 A

C. 3 A

D. 1 A

E. 5 A

2. In the circuit shown, the capacitance absorbs -200 VAR. Determine the average power dissipated in *R*if *R*= 5 ?.

A. 57.1 W

B. 80 W

C. 44.4 W

D. 66.7 W

E. 50 W

3. Determine **I****X**assuming **I****SRC**= *j*A.

A. *j*6 A

B. -*j*3 A

C. *j*3 A

D. *-j*6 A

E. *j*4 A

4. Determine the resistance between nodes a and b assuming that all resistances are 1 ?.

A. 4 ?

B. 2.4 ?

C. 3.2 ?

D. 1.6 ?

E. 0.8 ?

5. Two coils are tightly coupled to a high-permeability core, so that the leakage flux is negligibly small. If coil 1 has 100 turns and an inductance of 10 mH, and the mutual inductance is 12.5 mH, determine the number of turns of coil 2.

A. 125

B. 250

C. 150

D. 175

E. 200

6. Determine the inductance of coil 2 of the preceding problem.

A. 22.5 mH

B. 30.63 mH

C. 15.63 mH

D. 40 mH

E. 50.63 mH

7. A D’Arsonval movement has a resistance of *R*? and a full-scale deflection of 100 ?A. Determine the shunt resistance that will result in a full-scale deflection of 150 ?A, assuming *R*= 50 ?.

A. 150 ?

B. 200 ?

C. 300 ?

D. 100 ?

E. 250 ?

8. When a 9950 ? resistance is connected in series with a D’Arsonval movement of unknown resistance and full-scale deflection current, a voltage of 1 V across the series combination gives a certain full-scale deflection. If an additional 10,000 ? is connected in series with the combination, 2 V are required for full-scale deflection. Determine the resistance of the D’Arsonval movement.

A. 150 ?

B. 100 ?

C. 75 ?

D. 125 ?

E. 50 ?

9. Determine *L**eq*if *L*= 1 H.

A. 6 H

B. 4 H

C. 8 H

D. 7 H

E. 5 H

10. Determine **V****Th**, assuming **V****SRC**= 1?0° V

A. -1?0° V

B. 1?0° V

C. -2?0° V

D. 2?0° V

E. 4?0° V

11. Determine *Z**L*for maximum average power delivered to it if *R*= 5 ? and **I****X**= *k*?-45° where *k*= 2 A rms.

A. 10 + *j*10 ?

B. 5 + *j*5 ?

C. 5 – *j*5 ?

D. 10 – *j*10 ?

E. 15 – *j*15 ?

12. Determine the maximum average power delivered to *Z**L*in Problem 11, assuming that *R*= 5 ? and **I****X**is as in Problem 11.

A. 90 W

B. 200 W

C. 320 W

D. 180 W

E. 245 W

13. Load *L*1 absorbs 15 kVA at 0.6 p.f. lagging, whereas Load *L*2absorbs 4.8 kW at 0.8 p.f. leading. If **V****SRC**= 200?0° V rms at *f*= 50 Hz, determine the capacitor that must be connected in parallel with *L*1 and *L*2to have maximum magnitude of current through the source.

A. 0.67 mF

B. 0.55 mF

C. 0.34 mF

D. 0.46 mF

E. 1.24 mF

14. A periodic current is shown, where over a period,

*i*= 6 + *A*sin2*t*0 ? t ? ?

*i =*-4 + *A*sin2(*t*– ?) ? 0 ? t ? 2?

Determine the rms value of *i*if *A*= 1 A.

A. 5.83 A

B. 5.15 A

C. 6.20 A

D. 5.29 A

E. 5.52 A

15. The current waveform of the preceding problem is applied to a 2 ? resistor in parallel with a very large capacitor. Determine the voltage across the parallel combination.*t*?6*A*2?-4*A*

A. 2.5 V

B. 2 V

C. 3 V

D. 4 V

E. 3.5 V

16. The period of a periodic function *f*(*t*) is defined as:

*f*(*t*) = cos(*t*+ ?) – 2, -? *< t <*-?/2

*f*(*t*) = -cos(*t*) + *k*, -?/2 *< t <*+?/2

*f*(*t*) = cos(*t*– ?) – 2, ?/*2 < t <*?

Derive the trigonometric Fourier series expansion of *f*(*t*), assuming *k*= 3.

17. Given *v**SRC*= cos*t*V and *i**SRC*= sin2*t*A.

6% (a) Derive the expression for *i**X*in the time domain.

5% (b) Determine the power dissipated in the resistor.

18. Given the circuit shown, with *a*= 1.

3% (a) Determine the current in the capacitor

2% (b) Replace the capacitor by a current source, in accordance with the substitution theorem

3% (c) Rearrange the current source as two current sources across the transformer windings

3% (d) Determine **I****SRC**.

19. Determine *X*and *R*for maximum power transfer to *R*and calculate this power.

20. Determine the complex power delivered by each source given that **V****SRC**= 5cos?*t*, **I****SRC**= -2sin?*t*, and assuming *Z**L*= *k*(1 – *j*) where *k*= 1.