Electrical Engineering Fundamentals

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1 Electrical Engineering Fundamentals EE-238 Sheet 1 Series Circuits 1- For the circuits shown below, the total resistance is specified. Find the unknown resistance and the current for each circuit k Ω R 60 V R T = 60 k Ω 120V 50 Ω R 1 60 Ω R T = 220 Ω 4.5 k Ω 0.4 k Ω R 1 = R 2 10 Ω 2- find the applied voltage E necessary to develop the current specified in each circuit below. 60 Ω 1.2 KΩ 1.2 Ω 8.2 Ω 4.7Ω = 4 ma E 2.74 KΩ E 2.7Ω = 250 ma 3- for each network, determine the current, the source voltage E, the unknown resistance and the voltage across each element. 5 Ω E P = 79.2 mw + E 12V 2 Ω 3.3 kω 2.2 kω R T =16 Ω R R + 9 V 1

2 4- find the unknown voltage source and resistor for each of the networks shown below. Also indicate the direction of tresulting current. E 5 KΩ P = 100 mw 6 V - 12 V + + R = 5 ma R 16 V 2 kω 8 V _ 20 V E 5- find the unknown quantites in the circuits shown below. + V V V + -- V Ω R 2..2 Ω 4.7 Ω V E 6.8 Ω V 2 + P = 8 W P = 4 W + V V 2 -- P = 21 W - 20 Ω 1 Ω + R 1 R 2 E R V 3 E 1 Ω 1A _ R T =16 Ω 6- Using the voltage divider, find V ab for the circuits shown below. 4 K Ω 1 K Ω a 2.5 Ω a 1.5 Ω 40V 2 K Ω 3 K Ω Va b 0.36V 0.6 Ω V ab b 0.5 Ω b 0.7 Ω 2

3 Electrical Engineering Fundamentals Sheet 2 Parallel Circuits EE Using the information provided find the unkonown resistances in the following circuts. R T = 6 Ω 18 Ω R 18 Ω R T = 4 Ω R 1 9 Ω R 2 =R 1 18 Ω 6 A 12 V R 6 Ω 1 24 V 2- For the network shown: a- Find the current. b- Calculate the power dissipated by 4 Ω resistor. c- Find the current Ω 4Ω 12 Ω 2-8 V 3- For the network shown: a- Find the current. b- Find the voltage V. c- Calculate the source current s. -- V +24 V + S 10 K Ω 4 K Ω +8 V 2 K Ω 4- Using Kirchhoff s current law, determine the unknown current in the network shown below. 60 μa 5 ma 2 μa ma μa ma 8 ma 1 3

4 5- Find the unknown quantities for the circuits shown below. 64 V 3 =100 ma 1 3 1KΩ R 4KΩ P =30 W 1 3 E 30 Ω R 2 R 3 = R 2 2 A 6- Using the current divider rule, find the unknown currents for the networks shown. 1 1 Ω 2 Ω 500 ma Ω Ω 12 Ω Ω 1 = 4 A 7- Calculate the resistor R for the network shown, that will ensure the current 1 = KΩ 60 ma R 2 8- For the network shown, determine: a- The short circuit currents 1 and 2. b- The voltages V 1 and V 2. c- The source current. 2 4 Ω 10 Ω Ω V 1 20 V V Ω 4

5 Electrical Engineering Fundamentals EE-238 Sheet 3 Series &Parallel Kirchhoff s Laws 1- For the network shown: a- Calculate R T. b- Determine and 1. c- Find V Ω R T + 64 V 6 Ω V 3 12.Ω _ 2- For the circuit shown: a- Determine R T. b- Find s, 1 and 2. c- Calculate V a. s Ω 36V 10 Ω 15 Ω V a 2 Ω R T V a 14 Ω 6 Ω 4 20 Ω b 3- For the network shown: a- Determine the currents s, 1, 3 and 4. b- Calculate the voltages V a and V bc. c S 3 10 Ω 20 V 5 Ω 1 5

6 4- Find V o in the circuit shown. 1.5 A 300 Ω 2 KΩ 10 KΩ 200 Ω - V o Ω 1 KΩ 5- Find V o and V g in the circuit shown 16 Ω 2 Ω 6 Ω 15A 20 Ω 12 Ω Ω 30 Ω V o 32 Ω V g For the network shown: a- Determine the current. b- Calculate the open circuit voltage V. 8 Ω 20V + V - 8 V 3 Ω 6 Ω 6

7 Electrical Engineering Fundamentals EE-238 Sheet 4 Node Voltage Methode 1- Write the nodal equations of the networks shown below, then find the node voltages. 2Ω 5A 2Ω 5Ω 3A 4Ω 4Ω 4A 2Ω 2A 20Ω 5Ω 2- Use the node voltage methode to find the voltages V 1 and V 2 in the circuit shown. 8Ω + + 6A V 1 40Ω 80Ω V 2 120Ω 1A 3- Use the node voltage methode to find the voltages V 1 and V 2 in the circuit shown. 4Ω 80Ω V V 1 10Ω V 2 3A 5Ω 7

8 4- Use the node voltage methode to find the voltages a, b and c in the circuit shown. 5Ω 4Ω 10Ω a + b - c 128V 60 Ω 80 Ω 320V Use the node voltage methode to find the voltages 1 in the circuit shown. 4Ω 1 Ω 3 Ω V 2A 6Ω - 6- Find the voltage V x using the node voltage methode. 7 Ω 4 A + 4 Ω 6 A V x _ 5 Ω 3 Ω + - 2V 8

9 Electrical Engineering Fundamentals EE-238 Sheet 5 Mesh Current Method 1- Find the current through each resistor using mesh current method. 3.3 KΩ 5.6 KΩ 2.2 KΩ 30 V 10 V 20 V 1.2 KΩ 9V 8.2 KΩ 9.1 KΩ 6 V 1.1 KΩ 2- Using mesh current method find the voltages V ab for the networks shown. 6 V a 5Ω 2 Ω 3 Ω V ab 20 V 25 V 60 V b a 4 Ω 6 V b 3 A 3 Ω 6 Ω 8 Ω 4 V 9

10 3- Use the mesh current method find the voltage across the 20 Ω resistors in the circuit. 5 Ω 4 Ω V 20 Ω 80 V Ω 80 Ω 4- Use the mesh current method find the total power dissipated in the circuit. 4 A 3 Ω 1.8 Ω V 3 A 15 V Ω 1.2 Ω 5- Use the mesh current method find the current 1 in the circuits. 8 A 6 Ω 8 Ω 4 Ω 1 3 A 1 Ω 20 V 4 Ω 10 Ω 6 Ω 24 V 1 6 A 12 V 10

11 Electrical Engineering Fundamentals EE-238 Sheet 6 Source Transformation & Superposition 1-Using series of source transformation find o. 2.3 KΩ o 2 ma 1 KΩ 2.7 KΩ 0.6 ma 2- Using source transformation find V ab. 10 Ω 4 Ω a 6 A 24 V 12 Ω V ab b 3- Using series of source transformation find o. 1 A 6 Ω o 5 Ω 17 Ω 2 A 6 Ω Ω 34 V - 11

12 4- Using the principle of superposition find o. 12 Ω - V o + 10 V 6 Ω o 6 Ω 5 V 5- Using the principle of superposition find o. 3.3 K Ω o 5 ma 4.7 KΩ 8 V 4.7 KΩ 4 Ω o 6 A 3 Ω 6 Ω 12 Ω 4 Ω 12 V 8 V 6- Using the principle of superposition find o and V o. 4.5 Ω o 60 Ω 2 A 5 Ω 10 V _ + V o 20 Ω 5Ω 10 Ω _ + 12

13 Sheet 7 Magnetic Circuits 1- Find the current necessary to establish a flux Ф = 3x10-4 Wb in the series magnetic circuit shown in figure. L sheet steel = 0.3 m. L cast iron = 0.3 m. Area (throughout) =5x10-4 m 2. N =100 turns. Cast iron Sheet steel 0.3 m 0.3 m N =100 turns. 2- a- Find the number of turns N required to establish a flux Ф = 12x10-4 Wb in the magnetic circuit shown in figure. b- Find the permeability of the material. L m = mean length = 0.2 m. Uniform area (throughout) = m 2. =2A Cast steel =1 A N 2 =30 t N 1 Area = m 2 3- a -Find the m.m.f. N required to establish a flux Ф = lines in the magnetic circuit shown in figure. b- Find the permeability of each material. Cast-steel L cast steel =5.5 inch. L sheet steel = 0.5 inch. Uniform area (throughout) =1 inch 2. N Sheet- steel 4- For the series magnetic circuit with two sources of magnetic pressure, determine the current. Each applied m.m.f establishes a flux in the opposite direction of the other. Ф = 0.8x10-4 Wb. L cast steel =5.5 inch. L cast iron = 2.5 inch. Area (throughout) = 0.25 inch 2. Cast steel N 1 =20 t N 2 =30 t Cast iron 13

14 5- a -Find the current required to establish a flux Ф = 2.4x10-4 Wb in the magnetic circuit shown in figure. b- Compare the mmf drop across the air gap to that across the rest of the magnetic circuit. Discuss your results using the value of μ for each. Area (throughout) = 2 x10-4 m 2. N = 100 Turns. l ab = l cd = 0.05 m. l ac = l bd = 0.02 m. a b m c d 6- The magnetic circuit shown in figure is constructed of sheet steel, and the coil has 900 turns. Calculate the current required to establish a flux Ф = 330 μwb in the air gap. 12 cm 0.75 mm N 9cm 2x 3 c m 2 Cross- section areas 2x2 c m 2 7- Determine the magnetic flux Ф established in the magnetic circuit shown in figure. Area (throughout) =2 x10-4 m 2. l ab = l cd = 0.2 m. l ac = l bd =0.2 m. The air gap in l cd = 8x10-4 m. N =150 turns. µ r = 600. a b =2A 8x10-4 m c d 8- For the series - parallel magnetic circuit constructed of cast steel shown in figure, find the value of current required to establish a flux in the air gap Ф = 1x10-4 Wb. L ab = L bc =L fe= L ed =0.2 m. L af = L be= L= cd =0.1 m. N =200 t a Ф 1 b Ф 2 Ф 3 A=2x10-4 m 2 f e c d m Area =5x10-4 m 2 14

15 1- Convert the following: Sheet 8 Alternating Current Degrees to radians 45 o, 120 o,178 o, and 221 o Radians to degrees π / 8, 3 π, 0.55 π and 0.1 π / 4 2- Find the angular velocity ω of the waveforms with: Period T 2 sec,. 0.3 m sec, 4 μ sec and 1 / 25 sec. Frequency f 50 Hz, 600 Hz, 2 KHz, and MHz. 3- Find the frequency f and the period T of sin waves having the angular velocity ω: 754 rad/sec, 8.4 rad/sec, 6000 rad/sec and 1/16 rad/sec. 4- A sinusoidal waveform: Passes through an angle of 30 o in 5 msec, determine the angular velocity ω. f the frequency is f = 50 Hz, determine the time it will take to pass an angle 45 o. 5- Find amplitude and frequency of the following waveforms: 20 sin 377 t, 5 sin 754 t, 10 sin t,0.001 sin 9421 t and 7.6 sin 43.6 t. 6- Sketch the wave 5 sin 754 t with abscissa: Angle in degrees, angle in radians and time in seconds. 7- Determine the time t for the given α in the following: V =0.5 sin α t ( α = 72 o ) and V = 20 sin α t ( α = 1.2 π ). 8- Given V =30x10 2 sin α, determine the angle α when V= 6 mv. 9- f V = 40 v at α =30 o and t = 1 m sec., write the mathematical expression of the sinusoidal voltage. 10- Sketch the waves 50 sin (ω t+ 0 o ), 5 sin (ω t 60 o ) and 50 cos (ω t). 11- Find the phase relation of between: v(t) = 40 sin (ω t+ 50 o ) and i(t) =5 sin (ω t+ 40 o ) v(t) = 0.2 sin (ω t- 80 o ) and i(t) =0.1 sin (ω t -10 o ) v(t) = 20 cos (ω t- 30 o ) and i(t) =5 sin (ω t+ 60 o ) 12- Write the analytical expression for the waveform given in figure. 25 V f = 60 H z i (t) 2/3 π π/6 ωt A ωt

16 Sheet 9 Average & Effective Value 1- Find the average values of the waveforms shown in figure over one cycle. v (t) i (ma) t (s) t (sec) 2- Find the average value of the waveforms shown in figure over one cycle. V(t) 10V t (sec) -10V 3- Find the effective value of the following sinusoidal waveforms: v(t)=20 sin 754 t v(t)= 7.07 sin377 t i(t) =0.006 sin (400 t+20 o ) i(t) =16x10-3 sin (377 t-10 o ) 4- Write the sinusoidal expressions for voltages and currents having the following effective values at a frequency of 60 c/sec with zero phase shift: volt 70.7 volt 0.06 A 24 μa 5- Find the effective value of the wave form shown in figure over one cycle. v (t) t (sec) Find the effective value of the wave forms shown in figure over one cycle. v (t) t (sec) v (t) t (sec)

17 7- Find the effective and average values of the square waveform of figure over one cycle. v (t) t (sec) V f = 60 H z i (t) 2/3 π π/6 ωt A ωt

18 Sheet 10 Phasors 1- Express the following phasor currents and voltages as sin waves if the frequency is f = 50 c/sec: a) = 40 A 20 o b) V = 120 v 0 o c) = 8 x10 3 A 120 o d) V = 5 v 90 o e) = 1200 A -120 o f) V = 6000 v -180 o 2- For the circuit shown in figure, find the sinusoidal expression for the unknown voltage v a if: e in = 60 sin (377t + 20 o ) v b = 20 sin (377t) 2 e in + + v a + v b 3- For the circuit shown in figure, find the sinusoidal expression for the unknown current i s if: i i 1 = 20x10 6 sin (ωt + 90 o s ) i 1 i s i 2 = 20x10 6 sin (ωt - 60 o ) 4- Find the sinusoidal expression for the unknown voltage e in if: v a = 60 sin (ωt + 30 o ) v b = 30 sin (ωt - 30 o ) v c = 40 sin (ωt o ) e in + + v a + v b + v c 5- For the circuit shown in figure, find the sinusoidal expression for the unknown current i s if: i 1 = 6x10 3 sin (377t o ) i 2 = 8x10 3 sin (377t) i s i 3 = 2 i i 1 i 2 i 3 2

19 Sheet 11 Series Configuration 1- Calculate the total impedance of the circuit shown in figure. Express your answer in Rectangular and polar form, and draw the impedance diagram. R = 6.8 Ω R 1 = 2 Ω Xc = 6 Ω R 1 = 1 KΩ X L1 =3 KΩ Z it X L 6.8 Ω Z it R 2 8 Ω Z it R 2 4 KΩ X L2 = 7 KΩ 2- Find the type and impedance in Ohms of the series circuit elements that must be contained in the closed containers shown in figure for the indicated voltages and currents at the input terminals. Find the simplest series circuits that satisfy the indicated conditions = 60A 70 o = 20 ma 40 o = 0.2 A -60 o E =120 v 0 o? E =80 v 320 o? E =8 Kv 0 o? 3- For the circuit shown in figure: R = 8 Ω X L = 6 Ω + E 100v 20 o a- Find the total impedance Z in polar form. b- Draw the impedance diagram. c- Find the current and the voltages V R and V L in polar form. d- Draw the phasor of voltages V, V and V and the current. e- Verify Kirchhoff's voltage law around the closed loop. f- Find the average power delivered to the circuit. g- Find the power factor of the circuit and indicate whether it is leading or lagging. h- Find the sinusoidal expressions for the voltages and current if f = 60 c/sec. i- Plot the waveforms for the voltages and current on the same set of axes.

20 4- Given the network shown in figure: + V R + V C R C e(t) = 20sinωt 0.47 KΩ 0.1 μf f =1Kc/sec a- Determine Z it b- Find. c- Calculate V R and V L d- Find P and p.f. 5- For the circuit shown in figure: R = 8 Ω X L = 6 Ω X C = 10 Ω e(t) = 70.7 sin377t a- Find the total impedance Z in polar form. b- Draw the impedance diagram. c- Find the value of C in μf and the value of L in Henry. d- Find the current and the voltages V R,V L and V C in polar form. e- Draw the phasor diagram of voltages V R,V L and V C and the current. f- Verify Kirchhoff's voltage law around the closed loop. g- Find the average power delivered to the circuit. h- Find the power factor of the circuit and indicate whether it is leading or lagging. i- Find the sinusoidal expressions for the voltages and current. j- Plot the waveforms for the voltages and current on the same set of axes.

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