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Cork Institute of Technology
Higher Certificate in Engineering in Electrical Engineering -
Award
(NFQ Level 6)
Summer 2007
Electrical Engineering
(Time: 3 Hours)
Attempt Five Questions. Examiners:^ Mr. J. Hurley Mr. M. Hennessy Prof. E. McQuade
Q1. (a) An impedance of (1.665+j10.9) Ω is connected in series with two impedances of (12-j9) Ω and (8+j6) Ω, which are in parallel. Calculate the magnitude and power factor of the main current when the combined circuit is supplied at 30 V. Find also the voltage across each impedance. ( (b) The load taken from an a.c. supply consists of: (i) a load of 30kW at 0.85 power-factor lagging; (ii) a motor load of 20kVA at 0.6 power-factor lagging; (c) a load of 15kW at 0.75 power-factor lagging. Calculate the total load from the supply in kW and kVA and its power-factor. (7 marks) (c) What would be the kVAr rating of a capacitor to bring the power-factor to 0.95 lagging and how would the capacitor be connected? (3 marks)
Q2. (a) Explain the advantage of connecting the low-voltage winding of distribution transformers in star. (5 marks) (b) A factory has the following load with power factor of 0.85 lagging in each phase. Red phase 40 A, yellow phase 45 A and blue phase 60 A. If the supply is 400 V, three-phase, four-wire, calculate the current in the neutral and the total power. (15 marks)
Q3. (a) Give an expression for the time constant of a circuit consisting of a capacitor C in series with a resistor R. A resistor is connected in series with a capacitor across a 200 V d.c. supply. What is the voltage across the capacitor after one time constant? (5 marks) (b) A 10 μF capacitor is connected in series with a 100 kΩ resistor across a 1000 V supply. To what voltage is the capacitor charged when the charging current has decreased to 80% of its initial value? (6 marks) (c) What is the time taken for the current to decrease to 40% of its initial value? (4 marks) (d) What is the voltage across the resistor after 3 s? (5 marks)
Q4. (a)^ With the aid of a circuit diagram show that two wattmeters can be connected to read the total power in a three-phase, three-wire system. (5 marks) (b) Two wattmeters connected to read the total power in a three-phase system supplying a balanced load read 25 kW and 20 kW respectively. Calculate the total power and the power factor of the load. (10 marks) (c) Explain the significance of: (i) equal wattmeter readings, and (ii) a zero reading on one wattmeter. (5 marks)
Q5. (a) Explain with a circuit diagram how the short-circuit test is performed on a single phase transformer. What information can be got from the short-circuit test? (5 marks) (b) A single-phase transformer is rated at 1.8 kVA, 240 V/120 V. When the secondary terminals are open-circuited and the primary winding is supplied at normal voltage ( kV), the power taken is 18 W. When the secondary terminals are short-circuited, the power required to circulate full load current in the short-circuited secondary is 24 W. Calculate: (a) the efficiency of the transformer at full load, unity power factor; (b) the load at which maximum efficiency occurs; (c) the value of the maximum efficiency. (15 marks)
Useful Formulae
Parallel Circuit
Two Impedances in Parallel 1 2
1 2 Z Z
Z ZZ
T = +
Only when Z 1 and Z 2 are expressed in complex form.
Transients in RC-Networks
Time Constant (^) T = RC (s)
Charging Growth of voltage across a capacitor
− RC
t vc V 1 e (V)
RC
t e R
i = V^ − (A)
Discharging
= ^ RC − t vc V e (V)
RC
t e R
i = V^ − (A)
Three-Phase
Unbalanced Load (^) PT = P 1 + P 2 + P 3 (W)
Power Factor Correction Cap. kVAr = kW ( Tan θ 2 − Tan θ 1 )
Power Factor ApparentPo wer
= TruePower
Reactive Power= VISin θ (VArs)
True Power= VICos θ (W)
Apparent Power (^) = VI (VA)
Two Wattmeter Method
Total Power (^) W 1 (^) + W 2 (W)
1 2
W W
Tan W W
The Transformer
x 100 % OutputPower IronLosses CopperLosses
OutputPower
The Three-Phase Induction Motor
Synchronous speed Ns = 60f/p (r/min) f = frequency p = pairs of poles
Per Unit Slip s
s r N
s = N − N
Rotor Speed (^) N (^) r = Ns ( 1 − s ) (r/min)
Rotor Frequency (^) f (^) r = sf
Rotor EMF per phase at standstill (^) Er (V)
Rotor Reactance per phase at standstill (^) X (Ω)
Rotor Current per phase at standstill R^2 X^2
I Er r =^ + (A)
Rotor Power Factor at standstill R^2 X^2
Cos R
At Slip s Rotor EMF per phase at slip s (^) sE (^) r (V)
Rotor Reactance per phase at slip s (^) sX (Ω)
