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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2012/
Electrical Circuit Analysis
Module Code: ELEC
School: Mechanical, Electrical and Process Engineering
Programme Title: BEng Electrical Engineering Y
Programme Code: EELEC_7_Y
External Examiner(s): Ms. Mary Desmond Mr. Colm Murray Internal Examiner(s): Noel Mulcahy
Instructions: Answer All Questions. – Each question is worth 20 marks
Duration: 2 hours
Sitting: Semester 1 2012/
Requirements for this examination: Use of any Scientific Calculator capable of complex calculation is permitted.
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
Q1.
a. The admittance of a series circuit is (2.488710-3^ + j6.601610-3)S. Determine the values of the circuit components if the frequency is 50Hz. (5 marks) b. A 200V, 60Hz supply is connected across a coil of resistance 2 Ω and inductance 0.35H connected in parallel with a 20 Ω resistor. Determine in polar form: i. The total impedance of the circuit (6 marks) ii. The supply current (3 marks) iii. The supply phase angle (3 marks) iv. The phase angle of the current through the coil (3 marks)
Q2. a. How are commercial & industrial electrical energy customers encouraged to improve their power factor? (2 marks)
b. A small engineering workshop is supplied at single-phase and has the listed loads connected.
8kVAr of inductive heating at PF = 0.935 lag; 2.5kW of fluorescent lighting at PF = 0.97 lag; 4.2kW of motors on average PF = 0.74 lag; 3kVA of welding plant at PF = 0.82 lag. Calculate:
- the total load in kVA, ` (3 marks)
- the total kVAr supplied, (3 marks)
- the kVAr needed to improve the overall power factor to 0.95, (3 marks)
- the overall PF of the installation. (3 marks)
c. The following filter was constructed in a Lab Experiment.
100Vrms @ Variable Frequency
V out
100
10 F
Determine the output voltage when a 10V sinusoidal supply of the following frequencies is applied. i. 1 Hz. (3 marks) ii. 10 kHz. (3 marks)
Q3.
a. A relay coil has a resistance of 240 and the current required to operate the relay is 60mA. When the coil is connected to a 40V d.c. power supply the operating time between, switch-on and the start of the relay operation is 35ms. Calculate: i. the steady-state relay current; (2 Marks) ii. the time constant; (8 marks) iii. the coil inductance (2 marks) b. To increase the operating time delay for the relay a 200 resistor is connected in series with the existing 240 resistor. Determine the new time delay for the relay (8 marks)
Q5. The following loads are connected to a 3-phase 400 V 50Hz supply: Between R line and S line: A 22.5 load at a power factor of 1 Between S line and T Line: A 21.87 load at a power factor of 0.87 lagging Between T line and R Line: A 19.01 load at a power factor of 0.98 leading
a. Calculate the phase current for each load. (4 marks) b. Calculate the phase angle for each load. (2 marks) c. Determine each line currents flowing. (14 marks)
Useful Formula
Capacitive Reactance
......
1 1 C 2 X j C j f C
[]
Inductive Reactance (^) X (^) L j.. L j.... 2 f L []
Impedance (a)
Z XL XC R []
(b) Z R^2 XL X C ^2 []
(c) Z R j L j C []
Series Circuit:
(a) 2 2 VT ( V (^) L VC ) VR [V]
(b) Z
R
p. f . Cos (power factor)
Parallel Circuit: (a)
IT I 1 I 2 I 3 [A]
(b) EQUIVALENT
T T (^) Z
V
I [A]
(c) ACTUAL
INPHASE I
I
p. f. (power factor)
Power P V. I. Cos [W] (Single Phase Power)
Time Constant R
L
[s]
Energy stored in an Inductor..^2 2
E LI [J]
^
t iL I e [A]
^
t iL I. e [A]
Star–Delta & Delta-Star Transform
A B C
A B Z Z Z
Z Z Z
1 , A B C
B C Z Z Z
Z Z Z
2 , A B C
A C Z Z Z
Z Z Z
3
2
1 * 2 2 * 3 3 * 1 Z
Z Z Z Z Z Z Z (^) A , 3
1 * 2 2 * 3 3 * 1 Z
Z Z Z Z Z Z Z (^) B , 1
1 * 2 2 * 3 3 * 1 Z
Z Z Z Z Z Z ZC
Growth of Current in an Inductor in an RL Network
Decay of Current through an Inductor in an RL Network
