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Cork Institute of Technology
Higher Certificate in Engineering in Electrical Engineering – Award
(NFQ Level 6)
Autumn 2007
Electrical Engineering
(Time: 3 Hours)
Attempt Five Questions Examiners: Mr. John Hurley Mr. M. Hennessy Prof. E. McQuade
- (a) An impedance of (4.665+j7.9) 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 60 V. Find also the voltage across each impedance. (10 marks) (b) The load taken from an a.c. supply consists of: (i) a load of 40kW at 0.8 power-factor lagging; (ii) a motor load of 20kVA at 0.6 power-factor lagging; (c) a load of 25kW 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)
- (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 0.9 lagging in each phase. Red phase 60 A, yellow phase 50 A and blue phase 40 A. If the supply is 400 V, three-phase, four-wire, calculate the current in the neutral and the total power. (15 marks)
- (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 100 V d.c. supply. What is the voltage across the capacitor after one time constant? (6 marks) (b) A 50 μF capacitor is connected in series with a 2 MΩ 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? (8 marks) (c) What is the time taken for the current to decrease to 40% of its initial value? (6 marks)
- (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 5 kW respectively after the connections to the current coil of the second wattmeter have been reversed. 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)
- (a) Explain with a circuit diagram how the open-circuit test is performed on a single phase transformer. What information can be got from the open-circuit test? (5 marks) (b) A single-phase transformer is rated at 2.0 kVA, 240 V/120 V. When the secondary terminals are open-circuited and the primary winding is supplied at normal voltage ( V), 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 30 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)
