EEU104 Tutorial 1 Chapter 2, Pg 29 Exercises 20,21 as question (2 and 3) th Hughes Electrical & Electronic Technology 9 Ed Prentice Hall 1. a. The charge flowing in a wire is plotted in Figure 1. Sketch the corresponding current.
b. The total v v across a device and the current i through it are 0.5 ) A Calculate; v(t ) 5 cos(2t )V , i (t ) 10(1 e i). the total charge in the device at t 1sec ii). The power consumed by the device at t 1sec . −
=
=
t
−
=
=
2.
(a) An electric motor runs at 600 r/min when driving a load requiring a torque of 200Nm. If the motor input is 15kW, calculate the efficiency of the motor and the heat lost by the motor per minute, assuming its temperature to remain constant. (b) An electric kettle is required to heat 0.5 kg of water from 10 oC to boiling point in 5 min , the supply voltage being 230 V. If the efficiency of the kettle is 0.80, calculate the resistance of the heating element. Assume the specific heat capacity of water to be 4.2 kJ/kg K.
3.
A pump driven by an electric motor lifts 1.5m of water per minute to a height of 40 m. The pump has an efficiency of 90
3
per cent and the motor an efficiency of 85 per cent. Determine : (a) the power input to the motor; (b)the current taken from a 480 V supply; (c) the electrical energy consumed when the 3 motor runs at this load for 8 h. Assume the mass of 1 m of water to be 1000 kg.
EEU104 Tutorial 2 Chapter 3, Pg 58-60 Exercises 3, 7 & 16 th Hughes Electrical & Electronic Technology 9 Ed Prentice Hall 1.
Three lamps are connected in series across a 120V supply and take a current of 1.5 A. If the resistance of two of the lamps is 30Ω each, what is the resistance of the third lamp?
2.
Three resistors of 6Ω, 9Ω, 15Ω are connected in parallel to a 9V supply. Calculate: a). the current in each branch of the network; b). the supply current; c). the total effective resistance of the network.
3.
For the two circuits below; a. From Figure 1, use KCL to find the branch currents I 1 to I 4. b. From Figure 2, use KVL to find the branch voltages V 1 to V 4.
Figure 1
4.
Figure 2
A load taking 200A is supplied by copper and aluminium cables connected in parallel. The total length of conductor in each cable is 200m, and each conductor 2 has a cross sectional area of 40mm . Calculate: a. The voltage drop in the combined cables b. The current carried by each cable c. The power wasted in each cable Take the resistivity of copper and aluminium as 0.018μΩm and 0.028μΩm respectively.
EEU104 Tutorial 3 Chapter 4 th Hughes Electrical & Electronic Technology 9 Ed Prentice Hall
1.
A network is arranged as shown in Fig. A. Calculated the value of the current in the 8 Ω resistor by (a) the kirchhoff’s law . 5Ω
12Ω
10Ω
4V
15Ω
8Ω
6V
Fig. A
2.
Calculate the value of the current through the 40 in Fig B 20Ω
5Ω
4V
5Ω
40Ω
Fig. B
Ω
resistor
3. Using mesh analysis, calculate the current through the 15 Ω resistor in Fig. C 5Ω
6V
5Ω
20Ω
15Ω
10Ω
Fig. C
4.
Figure D shows a network of resistors. Find the equivalent resistance between node A and B
Fig. D
EEU104 Tutorial 4 Chapter 4, Pg 90-91 Exercises 6, 11 & 19 th Hughes Electrical & Electronic Technology 9 Ed Prentice Hall
6
A network is arranged as shown in Fig. A. Calculated the value of the current in the 8 Ω resistor by (a) the Nodal analysis, (b) Thevenin theorem and (c) superposition theorem. 5Ω
4V
12Ω
10Ω
15Ω
6V
8Ω
Fig. A
10
Using Thevenin theorem, calculate the current through the 10 W resistor in Fig. F 5Ω
6V
5Ω
20Ω
Fig. F
15Ω
10Ω
19
For the network shown in Fig. H, calculate the potential difference VNO. Calculate the resistance of a resistor connected across NO that would draw a current of 1.0 A
10V
10Ω
O 30V
N 20V
20Ω
Fig. H
20Ω
EEU104 Tutorial 5 Chapter 5, Pg 130 Exercises 30,32,34 & 36 th Hughes Electrical & Electronic Technology 9 Ed Prentice Hall
30
Define the time constant of a circuit that includes a resistor and capacitor connected in series A 100 μF capacitor is connected in series with an 800 Ω resistor. Determine the time constant of the circuit. If the combination is connected suddenly to a 100V d.c. supply. Find: (a) the initial rate of rise of p.d. across the capacitor; (b) the initial charging current; (c) the ultimate charge in capacitor; and (d) the ultimate energy stored in the capacitor.
32
A 2 μF capacitor is joined in series with a 2 M Ω resistor to a d.c. supply of 100V. Draw a current-time graph and explain what happens in the period after circuit is made, if the capacitor is initially uncharged. Calculate the current flowing and the energy stored in the capacitor at the end of the interval of 4s from the start.
34
Derive an expression for the stored electrostatic energy of a charged capacitor. A 10 μF capacitor in series with a 10 k Ω resistor is connected across a 500V d.c. supply. The fully charged capacitor is disconnected from the supply and discharged by connecting a 1000 Ω resistor across its terminal. Calculate: (a) the initial value of the charging current; (b) the initial value of the discharge current; and (c) the amount of heat, in joules, dissipated in the 1000 Ω resistor.
36
A circuit consisting of a 6 μF capacitor, an electrostatic voltmeter a resistor in parallel , is connected across a 140 V d.c. supply. It is then disconnected and the reading on the voltmeter falls to 70 V in 127 s. When the test is performed without the resistor, the time taken for the same fall in voltage is 183 s. Calculate the resistance of the resistor.
EEU104 Tutorial 6 Chapter 6, Pg 146 Exercises 13 Chapter 8, Pg 194 Exercises 19, 21 & 22 th
Hughes Electrical & Electronic Technology 9 Ed Prentice Hall
6.13 A short coil of 200 turns surrounds the middle of a bar magnet. If the magnet sets up a flux of 80 μWb, calculate the average value of the e.m.f induced in the coil when the later is removed completely from the influence of the magnet in 0.05 s.
8.19 A coil wound with 500 turns has a resistance of 2 Ω. It is found that a current of 3A produces a flux of 500 μWb. Calculate: (a) the inductance and time constant of the coil; (b) the average emf induced in the coil when the flux is reversed in 0.3 sec. If the coil is switched across a 10V d.c. supply, derive graphically a curve showing the growth of the current, assuming the inductance to remain constant.
8.21 The field winding of a d.c. machine has an inductance of 10H and takes a final current of 2A when connected to a 200V d.c. supply. Calculate: (a) the initial rate of growth of current; (b) the time constant; and (c) the current when the rate of growth is 5 A/s.
8.22 A 200V d.c. supply is suddenly switched across a relay coil which has a time constant of 3 ms. If the current in the coil reaches 0.2 A after 3 ms, determine the final steady value of the current and the resistance and inductance of the coil. Calculate the energy stored in the magnetic filed when the current has reached its final steady value.
1
EEU104 Tutorial 7 Chapter 9, Pg 220-221 Exercises 15,21,23 & 25 th Hughes Electrical & Electronic Technology 9 Ed Prentice Hall
15
Explain what is meant by the r.m.s value of the alternating current In a certain circuit supplied from 50Hz mains, the potential difference has a maximum value of 10A. At the instant t=0, the instantaneous values of the p.d. and the current are 400V and 4A respectively, both increasing positively. Assuming sinusoidal variation , state trigonometrical expression for the instantaneous values of the p.d. and the current at time t. Calculate the instantaneous values at the instant t=0.015 s and find the angle of phase difference between the p.d. and the current. Sketch the phasor diagram.
21
The voltage drops across two components, when connected in series across an a.c. supply, are: v1= 180 sin 314t volts and v2 = 120 sin (314t +π /3) volts respectively. Determine with the aid of a phasor diagram: (a) the voltage of the supply in trigonometric form; (b) the r.m.s. voltage of the supply; (c) the frequency of the supply.
23
Find graphically or otherwise the resultant of the following four voltages: e1=25 sin ωt ; e2=30 sin (ωt +π /6); e3= 30 cos ωt ; e4= 20 sin ( ωt -π /4). Express the answer in a similar form.
24
The currents in three circuits connected in parallel to a voltage source are: (a) 4A in phase with the applied voltage; (b) 6A lagging the o o applied voltage by 30 ; (c) 2A leading the applied voltage by 45 . Represent these currents to scale on a phasor diagram, showing their correct relative phase displacement with each other. Determine, graphically or otherwise, the total current taken from the source, and its phase angle with respect to the supply voltage.
EEU104 Tutorial 8 Chapter 10, Pg 241-242 Exercises 5,14,15 & 17 th Hughes Electrical & Electronic Technology 9 Ed Prentice Hall
5
A coil of inductance 0.1 H and negligible resistance is connected in series with a 25 Ω resistor . The circuit is energized from 230 V, 50 Hz source. Calculate (a) the current in the circuit; (b) the p.d. across the coil ; (c) the p.d. across the resistor; the phase angle of the circuit. Draw to scale a phasor diagram representing the current and the component voltages.
14
A single-phase network consists of three parallel branches, the currents in the respective branches being represented by : i1 = 20 sin 314t amperes ; i2 =30 sin (314t – π /4) amperes ; and i3 = 18 sin (314t + π /2) amperes. (a) Using a scale of 1 cm = 5A, draw a phasor diagram and find the total maximum value of the current taken from the supply and the overall phase angle; (b) Express the total current in a form similar to that of the branch currents; (c) If the supply voltage is represented by 200 sin 314t volts, find the impedance, resistance and reactance of the network.
15
A non-inductive resistor is connected in series with a coil across a 230 V, 50Hz supply. The current is 1.8A and the potential difference across the resistor and the coil are 80 V and 170V respectively. Calculate the inductance and the resistance of the coil, and the phase difference between the current and the supply voltage. Also draw the phasor diagram representing the current and the voltages.
17
A coil having a resistance of 15 Ω and an inductance of 0.2 H is connected in series with another coil having a resistance of 25 Ω and an inductance of 0.04 H to a 230 V, 50 Hz supply. Draw to scale the complete phasor diagram for the circuit and determine: (a) the voltage across each coil; (b) the active power dissipated in each coil ; (c) the power factor of the circuit as a whole.
EEU104 Tutorial 9 Chapter 11, Pg 258 Exercises 2,3,8 & 11 th Hughes Electrical & Electronic Technology 9 Ed Prentice Hall
2
A 130 Ω resistor and a 30 μF capacitor are connected in parallel across a 200 V, 50Hz supply. Calculate : (a) the current in each branch; (b) the resultant current; (c) the phase difference between the resultant current and the applied voltage; (d) the active power; and (e) the power factor. Sketch the phasor diagram.
3
A resistor and a capacitor are connected in series across a 150V a.c. supply. When the frequency is 40Hz the current is 5 A, and when the frequency is 50 Hz the current is 6 A. Find the resistance and capacitance of the resistor and capacitor respectively. If they are now connected in parallel across the 150 V supply, find the total current and its power factor when the frequency is 50 Hz.
8
A coil, having a resistance of 20 Ω and an inductance of 0.0382 H, is connected in parallel with a circuit consisting of a 150 μF capacitor in series with a 10 Ω resistor. The arrangement is connected to a 230 V, 50 Hz supply. Determine the current in each branch and, sketching a phasor diagram, the total supply current.
11
Two circuits, A and B, are connected in parallel to a 115 V, 50 Hz supply. The total current taken by the combination is 10 A at unity power factor. Circuit A consists of a 10 W resistor and a 200 mF capacitor connected in series; circuit B consists of a resistor and inductive reactor in series. Determine the following data for circuit B: (a) the current; (b) the impedance; (c) the resistance; (d) the reactance.
EEU104 Tutorial 10 Chapter 12, Pg 272 Exercises 4,5 & 7 th Hughes Electrical & Electronic Technology 9 Ed Prentice Hall
4
A single phase motor takes 50A at a power factor of 0.6 lagging from a 230 V, 50 Hz supply. What value of the capacitance must a shunting capacitor have to raise the overall power factor to 0.9 lagging? How does the installation of the capacitor affect the line and motor current?
5
A 230 V, single phase supply feeds the following loads: (a) incandescent lamps taking a current of 8 A at unity power factor; (b) fluorescent lamps taking a current of 5 A at 0.8 leading power factor; (c)a motor taking a current of 7 A at 0.75 lagging power factor. Sketch the phasor diagram and determine the total current, active power and reactive power taken from the supply and overall power factor.
7
A cable is required to supply a welding set taking a current of 225 A at 110 V alternating current, the average power factor being 0.5 lagging. Av available cable has a rating of 175 A and it is decided to use this cable by installing a capacitor across the terminals of the welding set. Find : (a) the required capacitor current and reactive power to limit the cable current to 175 A; (b) the overall power factor with the capacitor in circuit.
EEU104 Tutorial 11 Chapter 13, Pg 288-289 Exercises 10,12,14 ,16 & 26 th Hughes Electrical & Electronic Technology 9 Ed Prentice Hall
10
Derive expressions, in rectangular and polar notations, for the admittances of the following impedances: (a) 10 + j15 Ω; (b) 20 – j10 o o Ω ; (c) 50 / 20 Ω ; (d) 10 / -70 Ω.
12
Calculate the resistance and inductance or capacitance in parallel for each of the following admittances, assuming the frequency to be 50 o o Hz: (a) 0.25 + j0.06 S; (b) 0.05 – j0.1 S; (c) 0.8 / 30 S; (d) 0.5 / -50 S.
14
A voltage , v= 150 sin (314t + 30o) volts, is maintained across a circuit consisting of a 20 W non-reactive resistor in series with a lossfree 100 mF capacitor. Derive an expression for the r.m.s. value of the current phasor on: (a) rectangular notation; (b) polar notation. Draw the phasor diagram.
16
The impedance of two parallel branches can be represented by (24+j18) Ω and (12-j22) Ω respectively. If the supply frequency is 50 Hz, find the resistance and inductance of each circuit. Also, derive a symbolic expression in a polar form for the admittance of the combined circuits, and thence find the phase angle between the applied voltage and the resultant current.
26
A p.d of 200 / 30 V is applied to two branches connected in parallel. o o The currents in the respective branches are 20 / 60 A and 40 / 30 A. Find the apparent power (in kVA) and the active power (in kW) in each branch and in the main network. Express the current in main network in the form A + jB.
o
EEU104 Tutorial 12 Chapter 15, Pg 337-338 Exercises 6,7,11 & 14 th Hughes Electrical & Electronic Technology 9 Ed Prentice Hall
6
Determine the Thevenin equivalent circuit for the network shown in Fig. F.
4Ω AC
6Ω 8Ω
25/ 0o V Fig. F 7
Determine the Thevenin equivalent circuit for the network shown in Fig. G
6Ω (1+j1)A
8Ω
4Ω
Fig. G 11
For the network shown in Fig . I, determine the Norton equivalent circuit.
100 Ω AC
(10+j20)V
50Ω
Fig. I
20 Ω
14 For the network shown in Fig. J, determine the current in RL. Use Norton’s theorem and nodal analysis.
5Ω AC
(25+j10)V
10Ω
20 Ω
Fig. J
RL=10Ω
EEU104 Tutorial 13 Chapter 34, Pg 667-668 Exercises 3, 9, 10, 12, 13 & 14 th Hughes Electrical & Electronic Technology 9 Ed Prentice Hall
3
Derive, for both star- and delta-connected systems, an expression for the total power input for a balanced three-phase load in terms of line voltage, line current and power factor. The star-connected secondary of the transformer supplies a deltaconnected motor taking a power of 90kW at a lagging power factor of 0.9. If the voltage between lines is 600V, calculate the current in the transformer winding and in the motor winding. Draw circuit and phasor diagrams, properly labeled, showing all voltages and currents in the transformer secondary and the motor.
9
Derive the numerical relationship between the line and phase currents for a balanced three-phase delta-connected load. Three coils are connected in delta to a three-phase, three wire, 400V, 50 Hz supply and take a line current of 0.5A 0.8 power factor lagging. Calculate the resistance and inductance of the coils. If the coils are star-connected to the same power, calculate the line current and the total power. Calculate the line currents if one coil becomes opencircuited when the coils are connected in star.
10
The load connected to a three-phase supply comprises three similar coils connected in star. The line currents are 25A and the apparent and active power inputs are 20kVA and 11 kW respectively. Find the line and phase voltages, reactive power input and the resistance and reactance of each coil. If the coils are now connected in delta to the same three-phase supply, calculate the line currents and the active power taken.
12
Explain the advantage of connecting the low-voltage winding of the distribution transformers in star. A factory has the following load with power factor of 0.9 lagging in each phase. Red phase 40A, yellow phase 50A and blue phase 60A. If the supply is 400 V, three-phase, four-wire, calculate the current in the neutral and the total active power. Draw a phasor diagram for phase
and line quantities. Assume that, relative to the current in the red o phase, the current in the yellow phase lags by 120 and that in the blue o phase leads by 120 . 13
A three-phase, 400 V system has the following load connected in delta: between the red and yellow lines, a non-reactive resistor of 100 W; between the yellow and the blue lines, a coil having a reactance of 60 W and negligible resistance; between the blue and the red lines, a loss-free capacitor having a reactance of 130 W. Calculate; (a) the phase currents; (b) the line currents. Assume the phase sequence to be R-Y, Y-B and B-R. Also, draw the complete phasor diagram.
14
The phase currents in a delta-connected three-phase load are as follows: between the red and yellow lines, 30A at p.f. 0.707 leading; between the yellow and blue lines, 20A at unity p.f.; between the blue and red lines, 25A at p.f. 0.866 lagging. Calculate the line currents and draw the complete phasor diagram.
EEU104 Tutorial 14 Chapter 35, Pg 702-703 Exercises 19,20, 21, 26 & 29 th Hughes Electrical & Electronic Technology 9 Ed Prentice Hall
19
The ratio of turns of a single-phase transformer is 8, the resistances of the primary and secondary windings are 0.85 Ω and 0.012Ω respectively, and the leakage reactances of these windings are 4.8 Ω and 0.07Ω respectively. Determine the voltage to be applied to the primary to obtain a current of 150 A in the secondary when the secondary terminals are short-circuited. Ignore the magnetizing current.
20
A single-phase transformer operates from a 230 V supply. It has an equivalent resistance of 0.1 Ω and an equivalent leakage reactance of 0.5 W referred to the primary. The secondary is connected to a coil having a resistance of 200 W and a reactance of 100 W. Calculate the secondary terminal voltage. The secondary winding has four times as many turns as primary.
21
A 10 kVA single-phase transformer, for 2000 V/400 V at no load, has a resistances and leakage reactances as follows: Primary winding : resistance, 5.5 Ω; reactance , 12 Ω. Secondary winding: resistance , 0.2 Ω; reactance , 0.45 Ω. Determine the approximate value of the secondary voltage at full load, 0.8 power factor (lagging), when the primary supply voltage is 2000 V.
26
A 230 V/400 V single-phase transformer absorbs 35 W when its primary winding is connected to a 230 V, 50 Hz supply, the secondary being on open circuit. When the primary is short circuited and a 10 V, 50 Hz supply is connected to the secondary winding, the power absorbed is 48 W when the current has the full-load value of 15 A. Estimate the efficiency of the transformer at half-load, 0.8 power factor lagging.
29
A single-phase transformer is rated at 10 kVA, 230 V/100 V. When the secondary terminals are open-circuited and the primary winding is supplied at normal voltage (230 V), the current input is 2.6 A at a power factor of 0.3. When the secondary terminals are short-circuited, a voltage of 18 V applied to the primary causes the full-load current (100 A) to flow in the secondary, the power input to the primary being 240 V. 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.
