PAPER CODE ........ELEC209............ PAGE .. ..... 1.............. OF ....9..........................CONTINUED.
FIRST SEMESTER EXAMINATIONS 2019/20

ELECTRICAL CIRCUITS & POWER SYSTEMS

TIME ALLOWED: Three Hours

INSTRUCTIONS TO CANDIDATES

The numbers in the right hand margin represent an approximate guide to the marks available for that
question (or part of a question). Total marks available are 100.

Formula Table

PAPER CODE NO. EXAMINER: Dr. A. Al-Ataby
ELEC209 DEPARTMENT: EE&E TEL. NO.: 48045

PAPER CODE ........ELEC209........ PAGE ...........2............... OF ................7..............CONTINUED

1. a) i)

State why in a three-phase system, transformers in the distribution and
local substations must have a secondary winding connected as Y (start)
rather than Δ (delta).

2
ii)

State, with a proper justification, a possible and quick way to check if
there is a fault in a three-phase system that is arranged as four-wire Y.

2
b) i) A three-phase Y-connected load is supplied by a balanced three-phase
Y-connected source with a phase voltage of 120 V. If the line
impedance and load impedance per phase are 1 + j1 Ω and 20 + j10 Ω,
respectively, determine the line currents and load voltages.

6
ii) A balanced three-phase delta-connected load with per phase impedance
10 + j7.54 Ω is connected to a balanced three-phase Y voltage source
with phase voltage of 220 V. Determine the line currents and load
(phase) currents.

6
c) Two three-phase balanced loads are connected to a 240 kV line. Load 1 draws
30 kW at a power factor of 0.6 lagging, while load 2 draws 45 kVAR at a
power factor of 0.8 lagging.

i) Calculate the complex power consumed by each three-phase load.

4
ii) Calculate the total apparent power consumed by both three-phase loads.

2
iii) Calculate the line currents drawn by each load.

3
Total
25
PAPER CODE ........ELEC209........ PAGE ...........3............... OF ................7..............CONTINUED
2. a) It is required to measure the mutual inductance M formed between two coils
practically. With the aid of suitable circuit diagrams and equations, design a
laboratory experiment to fulfil this requirement.

4
b) For the transformer circuit shown in Figure Q2 below:

i) Find the input impedance of the transformer Zi.

2
ii) Find the primary voltage Ep and the secondary voltage Es.

5
iii) Find the currents in each loop of the transformer circuit.

2
c) A magnetically coupled pair has a resulting fluxes Φell1 and Φ21 are 0.3 mWb and
0.8 mWb, respectively. If the number of turns for each coil is to be selected as
N1 = 500 and N2 = 1000, design the magnetically coupled circuit (i.e. determine
L1, L2, M and the coefficient of coupling k) if the driving current is required to be
3 A.

8
d) The primary coil of a transformer is connected to a 6 V battery. The turns ratio is
1:3 and the secondary load, RL, is 100 ohms. Find the voltage across the load.

2
e) A transformer with N1 = N2 has a specific application in electrical engineering.
Briefly explain why it is needed in electrical system.
2
Total
25

PAPER CODE ........ELEC209........ PAGE ...........4............... OF ................7..............CONTINUED
3. a) For the circuit shown in Figure Q3a:

Figure Q3

i) Calculate vC, iC, and vR1 at 0.5 s after the switch makes contact
with position 1.

6
ii) The circuit sits in position 1 10 minutes before the switch is moved
to position 2. How long after making contact with position 2 will it
take for the current iC to drop to 8 μA? How long will it take for vC
to drop to 10 V?

6
b) A 50 Hz alternating (sinusoidal) voltage supply with 100 V peak voltage
and 50o phase shift is suddenly applied to a circuit which consists of a
resistance R in series with an inductance L = 1 mH.

i) Design the circuit such that the transient has no effect on the circuit. 5
ii) With proof, re-design the circuit such that the maximum current in
the circuit due to transient does not exceed 80 A.

8

Total
25
PAPER CODE ........ELEC209........ PAGE ...........5............... OF ................7..............CONTINUED
4. a) A 20 MVA transformer with 11 kV and 66 kV primary and secondary
voltages, respectively, has a reactance of 0.242 ohms referred to the primary.
What is the per-unit reactance on the primary side? What is the per-unit
reactance referred to the secondary?

4
b) Part of a power system is illustrated in Figure Q4. Two synchronous
generators are connected in parallel to the same 6.6 kV bus-bars (Gl: 5 MVA,
0.2 pu; G2: 15 MVA, 0.3 pu). The feeder has a reactance of 0.05 Ω/km and is
40 km long. Select 75 MVA as a common power base. Determine generators
and feeder per-unit reactances for the given common power base and draw the
equivalent circuit of the system.

Figure Q4
8
c)

A 600 MVA synchronous generator is star-connected, with 4 poles and a
synchronous reactance of 3 Ω. It is supplying 500 MW to an infinite bus at 22
kV, 50 Hz and 0.9 pf (lagging). Calculate the excitation voltage Vo and the

5
d)

Classify overhead transmission lines according to their length and illustrate the
equivalent circuit for each class.

4
e) The turns ratio of a transformer is 20:1 and a peak primary current value of 10
A. Given that the coefficient of coupling k between the primary and secondary
coils is 0.6, calculate the secondary current and the referred load to the
primary side when the load connected to the secondary winding is + )110( j .
4

Total
25

G1
G2
Feeder
PAPER CODE ........ELEC209........ PAGE ...........6............... OF ................7..............CONTINUED
2
pu1 B1 B2
2
pu 2 B2 B1
Z S V
Z S V
= 
Formula Table

Φ = BA

v = L di/dt

λ = NΦ = Li

λ1=N1 Φ1 = N1 Φ11 + N1 Φ12

L1 i1= N1 Φ11

N1 Φ12 =M12 i2

N2 Φ21 =M21 i1

Voltage Ratio: V1/V2 = N1/N2

Current Ratio: I1/I2 = N2/N1

Impedance Ratio: Z1/Z2 = (N1/N2)
2

vC = Vf c+ (Vi - Vf) e
-t/τ , where τ = RC
iL = If + (Ii - If) e
-t/τ , where τ = L/R

f = n/60 × p/2

,

Volume =

( )sins mi I t  = + 
0 ( )1 4ln H/m.
4
d r
L
r

− 
= +  
END
1 1 1 2
2 2 2 1
V j L I j MI
V j L I j MI
 
 
= 
= 
21 12
11 22
k
 
 
= =
1 2
Mk
L L
=
( )
( )
R
t
L
s t mi i i I sin t Ae  

= + = + − +
( )t t tti e Ae Be
  − −= +0 
2 2
0   = −
0 = ( )
t
ti e A Bt
−= +
2
2
where
1
m
m
v
I
R L
C

=
 
+ − 
 

=

2
1
2221
1211
2
1
V
V

YY
YY
I
I

=

2
1
2221
1211
2
1
I
I

ZZ
ZZ
V
V

=

2
2
2221
1211
1
1
I
V

TT
TT
I
V
F/m
ln
2
C 0

 −
=
r
rd

Tscsc2
Tsc2
)( VjXRI
VZIVg
++

=
+

=
T
sceff
sceff
V
XR
jXR
I
)(
222
+
+
=

vA
3
2
1
vP =
1
2 R
s
R
Reff −

=
2B
1B
2pu
1pu
S
S
Z
Z
=