ay2012 - ma2009 - tutorials v3
TRANSCRIPT
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MA2009: tutorial T1
circuits fundamentalscircuits fundamentals
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T1 1: batteriesT1.1: batteries
• The capacity of a car battery is usually specified in ampere‐hours. A b tt t d t 100 A h h ld b bl t l 100 A• A battery rated at, say, 100 A‐h should be able to supply 100 A for 1 hour, 50 A for 2 hours, 25 A for 4 hours, 1 A for 100 hours or any other combination yielding a product of 100 A‐hours, or any other combination yielding a product of 100 Ah.a. How many coulombs of charge should we be able to draw from a
fully charged 100 A‐h battery?b. How many electrons?
answers:a)360x103C; b)224x1022
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T1 2: batteriesT1.2: batteries
Th h l h i Fi i• The charge cycle shown in Figure is an example of a two‐rate charge.
• The current is held constant at 50 mA for 5 h Then it is switched to 20mA for 5 h. Then it is switched to 20 mA for the next 5 h. Find:a The total charge transferred to thea. The total charge transferred to the
battery.b. The energy transferred to the
battery.
Hint: Recall that energy, w, is the integral of power, or P = dw/dt .gy, , g f p , /
answers:a)1260 Cb)1732.5 J
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T1 3: Kirchhoff’s lawsT1.3: Kirchhoff s laws
• apply KCL to find the unknown current in the following circuitsg
a) b)
answers:a)3Ab)‐3A
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T1 4: Kirchhoff’s lawsT1.4: Kirchhoff s laws
• apply KCL to find voltages v1 and v2
answers:a)v1=12Vb)v2=2V
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T1 5 : Ohm’s lawT1.5 : Ohm s law
• use Ohm’s law and KCL to determine the current in the circuit
I1I2
2
answers:a) I1= 6.66Ab) I2= 3.33A
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T1 6 : powerT1.6 : power
• For the circuit
– determine which components are absorbing power and which are delivering power
– is the conservation of power satisfied?• explain your answer YES (power is conserved)p y
C absorbs 25WD absorbs 30WE absorbs 20W
answers:A generates 60WB generates 15W
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MP2008: tutorial T2
node‐voltage and mesh‐currentnode voltage and mesh currentmethods
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T2 1: Kirchhoff’s lawsT2.1: Kirchhoff s laws
• use Kirchhoff’s Current Law (KCL) to determine the unknown currents in the circuit
• assumeI 2 AI0 = ‐2 AI1 = ‐4 AIS = 8 AVS = 12 VVS 12 V
AnswersI2 = 6A;I3 = 2A.
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T2 2: node voltage methodT2.2: node voltage methodAnswers14.23V; 4.6 V; ‐5.4 V
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T2 3:mesh current methodT2.3: mesh current methodAnswer23.9 V
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T2 4: look carefully at the circuitT2.4: look carefully at the circuitfind simple ways to determine the current I2 for p y 2both KCL and KVL cases
II2
Answer: 1.6A
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T2 5: Kirchhoff’s lawsT2.5: Kirchhoff s laws • For the circuit shown in the following Figure, determine: g g ,
a. The current I1, I2 and I3b. The power delivered by the 3 A current source and by the 12V
lvoltage source c. The total power dissipated by the circuit.
• Express I I and I as a function of V knowing that:
V1
• Express I1, I2 and I3 as a function of V1 knowing that:– R1 = 25 Ω , R2= 10 Ω, R3= 5 Ω , R4= 7 Ω
1
I3
I2
‐279 W (current source);‐6.2 W (voltage source);285.2W (tot dissipated)
Answers:I1 = 3A; I2 = ‐1.8A; I3 = ‐1.2A;PWR
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MP2008: tutorial T3
superpositionsuperpositionThevenin & Norton Equivalent
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T3 1: superpositionT3.1: superpositionAnswer5.99 V
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T3 2: equivalent resistorT3.2: equivalent resistor
fi d th i l t i t b th• find the equivalent resistance seen by the source and the current I in the circuit.
• Vs=12V, R0=4Ω, R1=2Ω, R2=50Ω, R3=8Ω, R4=10Ω,R5=12Ω, R6 = 6Ω .
Answers4.76; 139 mA
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T3 3: Thevenin equivalentT3.3: Thevenin equivalent
find the Thevenin equiv. resistance seen by resistor R5 in the circuit below and computer the Thevenin (open‐circuit) voltage and the Norton (short circuit) when R5 is the loadvoltage and the Norton (short‐circuit) when R5 is the load.
Answers22.92 ; ‐6.67 V; ‐291 mA
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T3 4: Thevenin & NortonT3.4: Thevenin & Norton
find the Thevenin equiv. resistance seen by resistor R5 in the circuit below and computer the Thevenin (open‐circuit) voltage and the Norton (short circuit) when R5 is the loadvoltage and the Norton (short‐circuit) when R5 is the load.
Answers:52 ; 12.8 V; 246 mA
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MP2008: tutorial T4
power transferpower transferenergy storagesignal measures
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T4 1:max power transferT4.1:max power transferAnswers:a)8; 4.5W; 50%b)600; 510.4mW; 50%
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T4 2: energy storageT4.2: energy storageAnswers:11.76J; 0J; 0.18J; 17.65J
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T4 3: capacitive currentsT4.3: capacitive currents
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T4 4: rms and averageT4.4: rms and average
• Find the ratio between the average and rmsvalues of the waveform in the figureg
voltage1V
voltage
time2s 4s
9V‐9V
Answer:‐0.625
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MP2008: tutorial T5
frequency responsefrequency response
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T5 1: complex numbersT5.1: complex numbers
• A complex number Z can be represented in various ways. Typically y yp y– Cartesian: Polar:– Polar:
• determine the Polar and Cartesian forms for the following complex numbers
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T5 2: cutoff frequencyT5.2: cutoff frequency53kHz
Answer:high‐passgain 2/3 (or ‐3.5dB)
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T5 3: RLC filtersT5.3: RLC filters
(a) (b)
(c) (d)
c)LPd)LP
Answera)HPb)HP
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MP2008: tutorial T6
transient analysis fortransient analysis for switched, 1st order circuits
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T6 1: 1st order circuitsT6.1: 1st order circuits
R1 = 5kR2 = 7kR3 = 3kL = 0.9mHVs = 10V
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T6 2: 1st order circuitsT6.2: 1st order circuits
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T6 3: initial conditionsT6.3: initial conditionsDetermine the initial and final conditions for the following circuitsDetermine the initial and final conditions for the following circuits, assuming a steady‐state condition at time t=0‐
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T6 4: initial conditionsT6.4: initial conditionsAnswer35.4 ms