Q5. a) A motor takes a current of 10 A when supplied from a 250 V ac supply. Assuming a power factor of 0.75 lagging find the power consumed. Find also the cost of running the motor for 10 weeks continuously if 1 kWh of electricity costs 7.20 GHR [5 marks] b) If four identical lamps are connected in parallel and the combined resistance is 100 Q, find the resistance of one lamp. [2 marks] c) The instantaneous voltage in an AC circuit at any time t seconds is given by: v = 100 sin (50лt - 0.523) V. Find: i. the peak-to-peak voltage, the periodic time, the frequency and the phase angle; [2 marks] ii. the voltage when t = 0; [1 mark] 111. the voltage when t = 8 ms_ [1 mark] iv. the time in the first cycle when the voltage is - 40 V; and [2 marks] V. the first time when the voltage is a maximum. [2 marks] d) A load takes 50 kW at a power factor of 0.8 lagging. Calculate the apparent power and the reactive power. Determine the capacitance required to reduce the reactive power to half of its original value if the load is operating from a 250-V, 50-Hz supply. [5 marks] Q4. a) What is meant by three-phase (3-0) electric power? [2 marks] b) State three advantages of 3-0 AC power over single-phase AC power. [3 marks] c) Three loads, each of resistance 50 are connected in star to a 400 V, 3-phase supply. Determine: i. The phase voltage; ii. The phase current; and 111. The line current. [1 mark] [1 mark] [1 mark] d) Three identical coils, each of resistance 10 Q and inductance 42 mH are connected to a 415 V, 50 Hz, 3-0 supply for 365 days. Determine the total energy dissipated (kWh) when the coils are connected: i. in star; and ii. in delta. [3 marks] [3 marks] e) Purely resistive loads of 24 kW, 18 kW and 12 kW are connected between the neutral and the red, yellow and blue phases respectively of a 3-0, four-wire system. The line voltage is 415 V. Calculate: The current in each line conductor (i.e., IR, IY and IB); and i. ii. The current in the neutral conductor. [3 marks] [3 marks] Q3. a) A transformer is a magnetic circuit. Explain why this is so. [2 marks] [2 marks] b) A transformer has a turns ratio of 2:7. Explain this to a layman. c) State two (2) advantages and two (2) disadvantages of an auto-transformer. [4 marks] d) A transformer has 800 primary turns and 2000 secondary turns. If the primary voltage is 160 V, determine the secondary voltage assuming an ideal transformer. [2 marks] e) An ideal transformer connected to a 250 V mains, supplies a 25 V, 200 W lamp. Calculate the transformer turns ratio and the current taken from the supply. [4 marks] f) A model-train transformer plugs into 120 V ac and draws 0.65 A while supplying 15 A to the train. Calculate: (i) the turns ratio of the transformer; (ii) the voltage present across the tracks; and (iii) the power transformed. [2 marks] [2 marks] [2 marks] 18. The impedance (Z) of a coil of resistance 4 Q and reactance 3 Q2 is: a) 72 b) 252 c) 50 d) 10 19. In electrical measurements, the unit of conductance is the: a) Ohm b) Mho c) Farad d) Coulomb 20. Electric companies use a larger unit of electrical energy; the kWh, which is equivalent to: a) 36 MJ b) 0.36 MJ c) 3.6MJ d) 360 MJ 13. A three-phase wye-connected load has a phase current of 25 A. How much current is flowing through the lines supplying the load? a) 25/√√3 A b) 25√3 A c) 25 A d) 25√2 A 14. A three-phase resistive load has a phase voltage of 240 V and a phase current of 18 A. What is the total energy consumed by this three-phase load in 10 h? a) 74.82 kWh b) 129.6 kWh c) 129600 kWh d) 43.2 kWh 15. An alternating current completes 4 cycles in 5 ms. What is its frequency? a) 20 Hz b) 125 Hz c) 800 Hz d) 0.02 Hz 16. In a simple series DC circuit, the following properties uniquely identify such a circuit. a) Same voltage drops across each series component but different currents b) Each series component has the same value of current and voltage c) Current is the same through each component but voltage drops are different d) Voltage drops are the same as the source emf for each series component 17. For a simple DC circuit in which components are all connected in parallel: a) Current through each component is the same b) Voltage across each component is the same as the source emf c) Both the current and voltage values are the same for each component d) None of the above 10. Assuming your ECG bill for the month of September 2016 was GHC 135. What is the quantity of electricity consumed for the month if ECG charges 30 pesewas/unit and the service charge is also GHC 15? a) 500 units b) 150 units c) 120 units d) 400 units 11. A three-phase delta connected load has 30 A of current flowing through each phase winding. How much current is flowing through each of the lines supplying power to the load? a) 30 √2 A b) 30 √3 A c) 30/√3 A d) 30 A 12. A three-phase delta connected load receives power from a supply of 560 V. How much voltage is dropped across each phase? a) 560 √3 V b) 560/√3 V c) 560 V d) 560√√2 V 5. In a RLC AC circuit, heat dissipation occurs through a) Both the resistor and capacitor b) Both the resistor and inductor c) All three circuit elements d) Only the resistor 6. In the derivation of the root mean square (RMS) value of a sine wave, we use the mean of the squares of the values (currents or voltages) because a) Over one cycle the average value is zero b) Over one cycle, the average value is too large c) Over one cycle, the average value is too small d) Over one cycle, the average value is constant. 7. A transformer is the main reason for the use of AC for electricity transmission. This is because a) It has a very high efficiency and requires little or no maintenance over a long time b) It is a very portable device c) It is a purely resistive circuit d) None of the above 8. The wiring in houses and buildings is arranged so all electric devices are in parallel. In this way if you disconnect one device, a) The current to the others is not interrupted b) The current to the others is interrupted c) The whole circuit becomes open d) A short circuit is created. 9. The effective resistance of an electric circuit that has a resistor R Q in series with 10 resistors connected in parallel each also of resistance R Q is: a) 10R b) 11RQ c) 0.1R 2 d) 1.1RQ 1. In Ghana, power is transmitted at a linear frequency of 50 Hz which is equivalent to an angular frequency of a) 314 s-1 b) 50s-¹ c) 314 rad s-1 d) 50 rad s-1 2. Electric current is simply the rate of flow of electric charge. Hence its unit could also be a) C/s b) J/s c) J/C d) A/s 3. To determine the average value of a symmetrical periodic waveform such as a sine wave, one can integrate the wave equation from: a) 0 to 2π b) -лtoл c) -π/2 to 3/2 d) - to 0 4. The power dissipated in a 1.5-k pure resistor when a voltage v = 200 sin gat volts is applied across it is: a) 300 kW b) 26.67 W c) 8.89 W d) 13.33 W Q1. a) A single-phase network consists of three parallel branches, the currents in the respective branches being represented by: i 20 sin 314t amperes; i2 30 sin (314t-π/4) amperes; is 18 sin (314t+π/2) amperes. The supply voltage for the network is also represented by 200 sin314t volts. Calculate: i. 11. 111. iv. The total current in a form similar to the branch currents; The impedance, resistance, and reactance of the network; The circuit ... current and ms. voltage in polar form; The apparent power supplied by the sources in polar form; [2 marks] [3 marks] [3 marks] [2 marks] V. The apparent power supplied by the sources in rectangular (complex) form; [2 marks] vi. The active power absorbed and the power factor of the source. [2 marks] b) An alternating voltage v has a periodic time of 20 ms and a maximum value of 200 V. When time t = 0, v=-75 volts. Deduce a sinusoidal expression for v. If this alternating voltage feeds a 5028° Q2 impedance load, deduce a sinusoidal expression for the current, į that is also generated. [6 marks] b) Determine the equivalent resistance, RT, of the circuit of Fig. Q2b. [6 marks] 15 k 6 k 3 k ww RT 10 k 4 k 8 k ww ww 6 k 2 k Fig. Q2b Note the resistance values are in ko.. c) Two resistors when connected in series to a 110-V line use one fourth the power that is used when they are connected in parallel. If one resistor is 1.6 ko. what is the resistance of the other? [4 marks] a) Q2. Use a delta-star conversion to find the current I in the unbalanced bridge circuit in Fig. Q2a if the source voltage is 150 V. Hence determine the rate of heat dissipation from the 9-Q resistor and also from the entire circuit into the surrounding environment. I Req V Ω 10 Ω 8 Ω Fig. Q2a 10 Ω w w 5 Ω 4Ω